U412A Polinomio 4 y 5 X = linspace(-3,3,12) Y = 3*sin (exp(-x/2)) Tabla de datos y sumatorias Sistemas de ecuaciones y soluciones Polinomio y grafica
Ajuste de polinomio grado 4 Tabla de datos X
y
ajuste
-3.000000000000000
-2.920519778316971
-3.136246520239999
-2.454545454545455
-0.801116507633982
-0.315671593136276
-1.909090909090909
1.552952540062045
1.485865423905590
-1.363636363636364
2.755325114338886
2.479172941092940
-0.818181818181818
2.993596785794432
2.857239518532725
-0.272727272727273
2.733489951018636
2.795233866231512
0.272727272727273
2.297864622225752
2.450504844095480
0.818181818181818
1.849415392302503
1.962581461930424
1.363636363636363
1.453251190259060
1.453172879441748
1.909090909090909
1.126641540056258
1.026168406234469
2.454545454545454
0.866737862471463
0.767637501813223
3.000000000000000
0.663849792906007
0.745829775582253
>> format long >> mc2 Elija los
valores de xlinspace(-3,3,12) xlinspace(-3,3, 12)
x =
Columns 1 through 8
-3.000000000000000 -2.454545454545455 0.272727272727273 0.818181818181818
Columns 9 through 12
-1.909090909090909
-1.363636363636364
-0.818181818181818
-0.272727272727273
1.363636363636363
1.909090909090909
Ingrese las parejas de los datos de
2.454545454545454
3.000000000000000
x3*sin (exp(-x/2))
y =
Columns 1 through 8
-2.920519778316971 -2.92051977831 6971 -0.801116507633982 -0.801116507633 982 2.297864622225752 1.849415392302503
1.55295254006 2045 1.552952540062045
2.7553251143 38886 2.755325114338886
0.866737862471463
0.663849792906007
2.99359678 2.993596785794432 5794432
Columns 9 through 12
1.453251190259060
1.126641540056258
elija el grado del polinomio4
O =
1.0e+004 *
0.001200000000000 0.00120000000000 0
-0.000000000000000 -0.000000000000 000
0.004254545454545 0.00425454545454 5
-0.000000000000000 -0.00000000000 0000
0.026898572501878 0.0268985725018 78
-0.000000000000000 -0.00000000000 0000
0.004254545454545 0.004254545454 545
-0.000000000000000 -0.0000000000000 00
0.026898572501878 0.02689857250187 8
-0.000000000000000 -0.0000000000000 00
0.004254545454545 0.00425454545454 5
-0.000000000000000 -0.000000000000 000
0.026898572501878 0.02689857250187 8
-0.000000000000000 -0.00000000000 0000
0.200566322469280 0.2005663224692 80
-0.000000000000000 -0.00000000000 0000
0.026898572501878 0.026898572501 878
-0.000000000000000 -0.0000000000000 00
0.200566322469280 0.20056632246928 0
-0.000000000000000 -0.0000000000000 00
0.026898572501878 0.02689857250187 8
-0.000000000000000 -0.000000000000 000
0.200566322469280 0.20056632246928 0
-0.000000000000000 -0.00000000000 0000
1.613431596510340 1.6134315965103 40
bb =
1.0e+002 *
0.145714885054841 0.112025559503709 0.012935635455847 1.145390165764610 -1.280641071645164
2.7334899 51018636 2.733489951018636
sistema = Sistema de
ecuaciones
1.0e+004 *
0.001200000000000 0.00120000000000 0
-0.000000000000000 -0.000000000000 000
0.004254545454545 0.00425454545454 5
-0.000000000000000 -0.00000000000 0000
0.026898572501878 0.0268985725018 78
0.001457148850548 0.00145714885054 8
-0.000000000000000 -0.00000000000 0000
0.004254545454545 0.004254545454 545
-0.000000000000000 -0.0000000000000 00
0.026898572501878 0.02689857250187 8
-0.000000000000000 -0.0000000000000 00
0.001120255595037 0.00112025559503 7
0.004254545454545 0.00425454545454 5
-0.000000000000000 -0.000000000000 000
0.026898572501878 0.02689857250187 8
-0.000000000000000 -0.00000000000 0000
0.200566322469280 0.2005663224692 80
0.000129356354558 0.00012935635455 8
-0.000000000000000 -0.00000000000 0000
0.026898572501878 0.026898572501 878
-0.000000000000000 -0.0000000000000 00
0.200566322469280 0.20056632246928 0
-0.000000000000000 -0.0000000000000 00
0.011453901657646 0.01145390165764 6
0.026898572501878 0.02689857250187 8
-0.000000000000000 -0.000000000000 000
0.200566322469280 0.20056632246928 0
-0.000000000000000 -0.00000000000 0000
1.613431596510340 1.6134315965103 40
-0.012806410716452 -0.01280641071 6452
Solucion sol =
2.649071560543259 -0.642661673276221 -0.351650193548361 0.143297154360733 -0.008388002357245
Polinomio 2.649071560543259 2.64907156054325 9 + 0.008388002357245*x.^4
-0.642661673276221*x -0.642661673276 221*x +
-0.351650193548361*x.^2 -0.3516501935483 61*x.^2 +
0.143297154360733*x.^3 0.143297154360733 *x.^3 +
-
Sumatorias de x sx'
ans =
1.0e+004 *
-0.000000000000000
x.^1
0.004254545454545
x.^2
-0.000000000000000 0.026898572501878
x.^3 x.^4
-0.000000000000000
x.^5
0.200566322469280
x.^6
-0.000000000000000
x.^7
1.613431596510340
x.^8
Sumatorias de y
1.0e+002 *
0.145714885054841
y
0.112025559503709
x*y
0.012935635455847
y*x.^2
1.145390165764610
y*x.^3
-1.280641071645164
y*x.^4
Ajuste de Polinomio a grado 5 mc2 Elija los
valores de xlinspace(-3,3,12) xlinspace(-3,3, 12)
x = Columns 1 through 8 -3.000000000000000 -2.454545454545455 0.272727272727273 0.818181818181818
-1.909090909090909
-1.363636363636364
2.454545454545454
3.000000000000000
-0.818181818181818
-0.272727272727273
2.99359678 2.993596785794432 5794432
2.7334899 51018636 2.733489951018636
Columns 9 through 12 1.363636363636363
1.909090909090909
Ingrese las parejas de los datos de
x3*sin(exp(-x/2)) x3*sin(exp(-x/2) )
y = Columns 1 through 8
-2.920519778316971 -2.92051977831 6971 -0.801116507633982 -0.801116507633 982 2.297864622225752 1.849415392302503
1.55295254006 2045 1.552952540062045
2.7553251143 38886 2.755325114338886
0.866737862471463
0.663849792906007
Columns 9 through 12 1.453251190259060
1.126641540056258
elija el grado del polinomio5 O = 1.0e+005 *
0.000120000000000 0.00012000000000 0
-0.000000000000000 -0.000000000000 000
0.000425454545455 0.00042545454545 5
-0.000000000000000 -0.00000000000 0000
0.002689857250188 0.0026898572501 88
-0.000000000000000 -0.00000000000 0000
-0.000000000000000 -0.00000000000 0000
0.000425454545455 0.000425454545 455
-0.000000000000000 -0.0000000000000 00
0.002689857250188 0.00268985725018 8
-0.000000000000000 -0.0000000000000 00
0.020056632246928 0.02005663224692 8
0.000425454545455 0.00042545454545 5
-0.000000000000000 -0.000000000000 000
0.002689857250188 0.00268985725018 8
-0.000000000000000 -0.00000000000 0000
0.020056632246928 0.0200566322469 28
-0.000000000000000 -0.00000000000 0000
-0.000000000000000 -0.00000000000 0000
0.002689857250188 0.002689857250 188
-0.000000000000000 -0.0000000000000 00
0.020056632246928 0.02005663224692 8
-0.000000000000000 -0.0000000000000 00
0.161343159651034 0.16134315965103 4
0.002689857250188 0.00268985725018 8
-0.000000000000000 -0.000000000000 000
0.020056632246928 0.02005663224692 8
-0.000000000000000 -0.00000000000 0000
0.161343159651034 0.1613431596510 34
-0.000000000000000 -0.00000000000 0000
-0.000000000000000 -0.00000000000 0000
0.020056632246928 0.020056632246 928
-0.000000000000000 -0.0000000000000 00
0.161343159651034 0.16134315965103 4
-0.000000000000000 -0.0000000000000 00
1.353048857058631 1.35304885705863 1
bb =
1.0e+003 *
0.014571488505484 0.011202555950371 0.001293563545585 0.114539016576461 -0.128064107164516 1.002229547669045
sistema = Sistema de ecuaciones…. (lo
tuve que reducir de tamaño para
que pudiera presentarse bien la tabla)
1.0e+005 * La última columna es la de los términos independientes 0.000120000000000 0.000120000000000
-0.00000000000 -0.000000000000000 0000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.000145714885055 0.000145714885055
-0.000000000000000 -0.000000000000000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
0.000112025559504 0.000112025559504
0.000425454545455 0.000425454545455
-0.0000000000 -0.000000000000000 00000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.000012935635456 0.000012935635456
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
0.001145390165765 0.001145390165765
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
-0.001280641071645 -0.001280641071645
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
1.353048857058631 1.353048857058631
0.010022295476690 0.010022295476690
Solucion sol =
2.649071560543261 -0.951161669565782 -0.351650193548362 0.286206717849582 -0.008388002357245 -0.012621939549015
Polinomio y2 = sol(1)+ x*sol(2) +sol(3)*x.^2 +sol(4)*x.^3 +sol(5)*x.^4 +sol(6)*x.^5 = Polinomio 2.64907156054326 2.64907156054326 -0.951161669565782x -0.951161669565782x -0.351650193548362x.^2 -0.351650193548362x.^2 0.286206717849582*x.^3 -0.008388002357245*x.^4 -0.012621939549015*x.^5 x*sol(2) +sol(3)*x.^2 +sol(4)*x.^3 +sol(5)*x.^4 +sol(6)*x.^5
+
Sumatorias de
x
1.0e+005 * -0.000000000000000
x
0.000425454545455
x.^2
-0.000000000000000
x.^3
0.002689857250188
x.^4
-0.000000000000000
x.^5
0.020056632246928 0.020056632246928 x.^6 -0.000000000000000 -0.000000000000000 x.^7 0.161343159651034 -0.000000000000000 1.353048857058631
x.^8 x.^9 x.^10
Sumatorias de yx 1.0e+003 *
0.014571488505484
y
0.011202555950371
xy
0.001293563545585
x.^2y
0.114539016576461
x.^3y
-0.128064107164516
x.^4y
1.002229547669045
x.^5y
>> [x;y;y2]' Tabla de datos X
y
y ajustada
-3.000000000000000
-2.920519778316971
-3.002173435159545
-2.454545454545455
-0.801116507633982
-0.547252376457052
-1.909090909090909
1.552952540062045
1.400546187945299
-1.363636363636364
2.755325114338886
2.596994743133328
-0.818181818181818
2.993596785794432
3.036003631973320
-0.272727272727273
2.733489951018636
2.876490281431784
0.272727272727273
2.297864622225752
2.369248428895213
0.818181818181818
1.849415392302503
1.783817348489831
1.363636363636363
1.453251190259060
1.335351077401359
1.909090909090909
1.126641540056258
1.111487642194758
2.454545454545454
0.866737862471463
0.999218285133998
3.000000000000000
0.663849792906007
0.611756690501803
MI PROGRAMA QUE USÉ
mc2
Hecho por Oscar Enrique Ureña Márquez % Nos entrega % x.^3 etc
desde le termino independiente hasta
x
...
1
x
x.^2
clear, x=input('Elija x=input( 'Elija los valores de x' ) A= length(x); y=input('Ingrese y=input( 'Ingrese las parejas de los datos de x' ) m=input('elija m=input( 'elija el grado del polinomio' ); gms=m*2; % es el grado maximo de la sumatoria if m==1 gms=2; for n=1:gms sx(n)=sum(x.^n); % Es la sumatoria de x del grado n end O=[A sx(1);sx(1) sx(2)] for l=0:m b(l+1) = sum(y.*x.^l); end bb=b' sistema=[O bb] sol=O\bb else for n=1:gms sx(n)=sum(x.^n);
% Es la sumatoria de
x del grado n
end B=sx; % es el vector de sumatorias de x grado n for j=1:m+1 if j==1 O=[A B(1:m)]; % haciendo exclusion en el primer renglon, y concatenamos el numero de datos con las sumatorias else O(j,:)=B((j-1):(j-1)+(m)); % j es el numero del renglon, en el renglon j ponemos los ciertos valores del vector B de sumatorias end end % format rational O
for l=0:m b(l+1) = sum(y.*x.^l); end bb=b' sistema=[O bb] sol=O\bb end %sy=sum(y); % ym= sy/A; % y media %t1 = sum((y-ym).^2); %t2 = sum((y-yecn).^2); % el y ecn es el que obtenemos de nuestro metodo, el y valores tabulados %r =sqrt((t1-t2)./t1)*100; %fprintf('\nr porcentual de orden 5 = %8.2f\n',r)
normal son los
%coef=[' 1 ' ' x ' ' x.^2 ' ' x.^3 ' ' x.^4 ' ' x.^5 ' ' x.^6 ' ' x.^7 ' ' x.^8 '] %repcon=1 %for l=0:m %repre([repcon repcon+1])= [sol(l+1) coef(l+1)]; %repcon=repcon+2; %end %format rational %repre
DESPUES DE USAR EL PROGRAMA, PARA VER LAS LAS VARIABLES ASIGNADAS b
Te presenta el vector de sumatorias de y*x.^n desde n=0 hasta el grado de polinomio de ajuste
sx Te presenta el vector de sumatorias de x.^n desde n=1 hasta hasta el grado de ajuste*2 sistema
te presenta el sistema de ecuaciones con todo y términos independientes (en la última columna)
sol Te presenta el vector solución del sistema de ecuaciones [x;y]’ tabla de datos x y iniciales
MI CODIGO EN MATLAB MATLAB
INTACTO
x=linspace(-3,3,12)
x =
Columns 1 through 8
-3.000000000000000 -3.000000000000000
-2.454545454545455 -2.454545454545455
-1.909090909090909 -1.909090909090909
-1.363636363636364 -1.363636363636364
1.909090909090909
2.454545454545454
3.000000000000000
-0.801116507633982 -0.801116507633982
1.552952540062045 1.552952540062045
2.755325114338886 2.755325114338886
1.126641540056258
0.866737862471463
0.663849792906007
-2.454545454545455 -2.454545454545455
-1.909090909090909 -1.909090909090909
-1.363636363636364 -1.363636363636364
1.909090909090909
2.454545454545454
3.000000000000000
-0.818181818181818 -0.818181818181818
-0.272727272727273 -0.272727272727273
0.272727272727273 0.272727272727273
0.818181818181818 0.818181818181818
2.993596785794432 2.993596785794432
2.733489951018636 2.733489951018636
2.297864622225752 2.297864622225752
1.849415392302503 1.849415392302503
-0.818181818181818 -0.818181818181818
-0.272727272727273 -0.272727272727273
0.272727272727273 0.272727272727273
0.818181818181818 0.818181818181818
Columns 9 through 12
1.363636363636363
>> y = 3*sin(exp(-x/2)) 3*sin(exp(-x/2))
y =
Columns 1 through 8
-2.920519778316971 -2.920519778316971
Columns 9 through 12
1.453251190259060
>> format long >> mc2 Elija los los
valores de xlinspace(-3,3,12) xlinspace(-3,3,12)
x =
Columns 1 through 8
-3.000000000000000 -3.000000000000000
Columns 9 through 12
1.363636363636363
Ingrese las parejas de los los datos de
x3*sin(exp(-x/2)) x3*sin(exp(-x/2))
y =
Columns 1 through 8
-2.920519778316971 -2.920519778316971
-0.801116507633982 -0.801116507633982
1.552952540062045 1.552952540062045
2.755325114338886 2.755325114338886
1.126641540056258
0.866737862471463
0.663849792906007
2.993596785794432 2.993596785794432
Columns 9 through 12
1.453251190259060
elija el grado del polinomio4
O =
12 *
*
*
18829/70
*
18829/70
*
18829/70 18829/70
*
*
18829/70 18829/70
*
18829/70
*
196555/98
*
306552/19
*
468/11
*
18829/70
34753/2385
18829/70
*
6139/548
468/11
468/11
468/11
196555/98
* 196555/98 *
bb =
34753/2385 6139/548 824/637 16150/141 -9989/78
sistema =
12 * 468/11
468/11 *
*
18829/70 18829/70
18829/70
*
sol =
* 18829/70 * 196555/98
* 196555/98 *
196555/98 * 306552/19
824/637 16150/141 16150/141 -9989/78
2.733489951018636 2.733489951018636
2.297864622225752 2.297864622225752
1.849415392302503 1.849415392302503
2710/1023 -705/1097 -2099/5969 977/6818 -78/9299
Elija los los
valores de xlinspace(-3,3,12) xlinspace(-3,3,12)
x =
Columns 1 through 10
-3
-27/11
-21/11
-15/11
-9/11
-3/11 -3/11
3/11
9/11
15/11 15/11
21/11 21/11
715/492
1201/1066
Columns 11 through 12
27/11
3
Ingrese las parejas de los los datos de
x3*sin (exp(-x/2)) (exp(-x/2))
y =
Columns 1 through 10
-2021/692
-1148/1433
1657/1067
4786/1737
2805/937
Columns 11 through 12
813/938
707/1065
elija el grado del polinomio4
O =
12 *
*
*
*
18829/70
*
18829/70 18829/70
*
*
18829/70 18829/70
*
18829/70
*
468/11
bb =
468/11
468/11
196555/98
196555/98 *
18829/70 * 196555/98 * 306552/19
1159/424
6349/2763
1265/684
34753/2385 6139/548 824/637 16150/141 -9989/78
sistema =
12
*
*
468/11
468/11
468/11
*
*
18829/70 18829/70
18829/70
*
* 18829/70 * 196555/98
*
18829/70
34753/2385
18829/70
*
6139/548
* 196555/98 *
196555/98 * 306552/19
824/637 16150/141 16150/141 -9989/78
sol =
2710/1023 -705/1097 -2099/5969 977/6818 -78/9299
>> format long >> mc2 Elija los los
valores de xlinspace(-3,3,12) xlinspace(-3,3,12)
x =
Columns 1 through 8
-3.000000000000000 -3.000000000000000
-2.454545454545455 -2.454545454545455
-1.909090909090909 -1.909090909090909
-1.363636363636364 -1.363636363636364
1.909090909090909
2.454545454545454
3.000000000000000
Columns 9 through 12
1.363636363636363
Ingrese las parejas de los los datos de
y =
x3*sin (exp(-x/2)) (exp(-x/2))
-0.818181818181818 -0.818181818181818
-0.272727272727273 -0.272727272727273
0.272727272727273 0.272727272727273
0.818181818181818 0.818181818181818
Columns 1 through 8
-2.920519778316971 -2.920519778316971
-0.801116507633982 -0.801116507633982
1.552952540062045 1.552952540062045
2.755325114338886 2.755325114338886
1.126641540056258
0.866737862471463
0.663849792906007
2.993596785794432 2.993596785794432
2.733489951018636 2.733489951018636
Columns 9 through 12
1.453251190259060
elija el grado del polinomio4
O =
1.0e+004 *
0.001200000000000 0.001200000000000
-0.000000000000 -0.000000000000000 000
0.004254545454545 0.004254545454545
-0.00000000000 -0.000000000000000 0000
0.026898572501878 0.026898572501878
-0.000000000000000 -0.000000000000000
0.004254545454545 0.004254545454545
-0.000000000000 -0.000000000000000 000
0.026898572501878 0.026898572501878
-0.0000000000000 -0.000000000000000 00
0.004254545454545 0.004254545454545
-0.000000000000 -0.000000000000000 000
0.026898572501878 0.026898572501878
-0.00000000000 -0.000000000000000 0000
0.200566322469280 0.200566322469280
-0.000000000000000 -0.000000000000000
0.026898572501878 0.026898572501878
-0.000000000000 -0.000000000000000 000
0.200566322469280 0.200566322469280
-0.0000000000000 -0.000000000000000 00
0.026898572501878 0.026898572501878
-0.000000000000 -0.000000000000000 000
0.200566322469280 0.200566322469280
-0.00000000000 -0.000000000000000 0000
1.613431596510340 1.613431596510340
0.001200000000000 0.001200000000000
-0.000000000000000 -0.000000000000000
0.004254545454545 0.004254545454545
-0.000000000000000 -0.000000000000000
0.026898572501878 0.026898572501878
0.001457148850548 0.001457148850548
-0.000000000000000 -0.000000000000000
0.004254545454545 0.004254545454545
-0.000000000000000 -0.000000000000000
0.026898572501878 0.026898572501878
-0.000000000000000 -0.000000000000000
0.001120255595037 0.001120255595037
0.004254545454545 0.004254545454545
-0.000000000000000 -0.000000000000000
0.026898572501878 0.026898572501878
-0.000000000000000 -0.000000000000000
0.200566322469280 0.200566322469280
0.000129356354558 0.000129356354558
-0.000000000000000 -0.000000000000000
0.026898572501878 0.026898572501878
-0.000000000000000 -0.000000000000000
0.200566322469280 0.200566322469280
-0.000000000000000 -0.000000000000000
0.011453901657646 0.011453901657646
0.026898572501878 0.026898572501878
-0.000000000000000 -0.000000000000000
0.200566322469280 0.200566322469280
-0.000000000000000 -0.000000000000000
1.613431596510340 1.613431596510340
-0.012806410716452 -0.012806410716452
bb =
1.0e+002 *
0.145714885054841 0.112025559503709 0.012935635455847 1.145390165764610 -1.280641071645164
sistema =
1.0e+004 *
2.297864622225752 2.297864622225752
1.849415392302503 1.849415392302503
sol =
2.649071560543259 -0.642661673276221 -0.351650193548361 0.143297154360733 -0.008388002357245
>> plot(x,y,'og') plot(x,y,'og') >> hold on >> y1=sol(1) +x*sol(2) +x.^2*sol(3) +x.^3*sol(4) +x.^4*sol(5)
y1 =
Columns 1 through 8
-3.136246520239999 -3.136246520239999
-0.315671593136276 -0.315671593136276
1.485865423905590 1.485865423905590
2.479172941092940 2.479172941092940
1.026168406234469
0.767637501813223
0.745829775582253
Columns 9 through 12
1.453172879441748
>> hold on >> plot(x,y1,'r') plot(x,y1,'r') >> gtext('Ajuste gtext('Ajuste de polinimio
grado 4')
>> [x;y]'
ans =
-3.000000000000000 -2.920519778316971 -2.454545454545455 -0.801116507633982 -1.909090909090909
1.552952540062045
-1.363636363636364
2.755325114338886
-0.818181818181818
2.993596785794432
-0.272727272727273
2.733489951018636
0.272727272727273
2.297864622225752
0.818181818181818
1.849415392302503
1.363636363636363
1.453251190259060
1.909090909090909
1.126641540056258
2.454545454545454
0.866737862471463
3.000000000000000
0.663849792906007
>> [x;y;y1]'
2.857239518532725 2.857239518532725
2.795233866231512 2.795233866231512
2.450504844095480 2.450504844095480
1.962581461930424 1.962581461930424
ans =
-3.000000000000000 -2.920519778316971 -3.136246520239999 -2.454545454545455 -0.801116507633982 -0.315671593136276 -1.909090909090909
1.552952540062045
1.485865423905590
-1.363636363636364
2.755325114338886
2.479172941092940
-0.818181818181818
2.993596785794432
2.857239518532725
-0.272727272727273
2.733489951018636
2.795233866231512
0.272727272727273
2.297864622225752
2.450504844095480
0.818181818181818
1.849415392302503
1.962581461930424
1.363636363636363
1.453251190259060
1.453172879441748
1.909090909090909
1.126641540056258
1.026168406234469
2.454545454545454
0.866737862471463
0.767637501813223
3.000000000000000
0.663849792906007
0.745829775582253
0.004254545454545 0.004254545454545
-0.000000000000000 -0.000000000000000
>> sx
sx =
1.0e+004 *
-0.000000000000000 -0.000000000000000
0.026898572501878 0.026898572501878
-0.000000000000000 -0.000000000000000
0.200566322469280 0.200566322469280
>> format rational >> sx
sx =
*
468/11
>> sx'
ans =
-1/562949953421312 468/11 -1/140737488355328 18829/70 -1/17592186044416 196555/98 -1/1099511627776 306552/19
*
18829/70
*
196555/98
*
306552/19
-0.000000000000000 -0.000000000000000
1.613431596510340 1.613431596510340
>> format long >> sx'
ans =
1.0e+004 *
-0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000 1.613431596510340
>> b
b =
1.0e+002 *
0.145714885054841 0.145714885054841
0.112025559503709 0.112025559503709
>> b'
ans =
1.0e+002 *
0.145714885054841 0.112025559503709 0.012935635455847 1.145390165764610 -1.280641071645164
Elija los los
valores de xlinspace(-3,3,12) xlinspace(-3,3,12)
x =
Columns 1 through 8
0.012935635455847 0.012935635455847
1.145390165764610 1.145390165764610
-1.280641071645164 -1.280641071645164
-3.000000000000000 -3.000000000000000
-2.454545454545455 -2.454545454545455
-1.909090909090909 -1.909090909090909
-1.363636363636364 -1.363636363636364
1.909090909090909
2.454545454545454
3.000000000000000
-0.818181818181818 -0.818181818181818
-0.272727272727273 -0.272727272727273
0.272727272727273 0.272727272727273
0.818181818181818 0.818181818181818
2.993596785794432 2.993596785794432
2.733489951018636 2.733489951018636
2.297864622225752 2.297864622225752
1.849415392302503 1.849415392302503
Columns 9 through 12
1.363636363636363
Ingrese las parejas de los los datos de
x3*sin(exp(-x/2)) x3*sin(exp(-x/2))
y =
Columns 1 through 8
-2.920519778316971 -2.920519778316971
-0.801116507633982 -0.801116507633982
1.552952540062045 1.552952540062045
2.755325114338886 2.755325114338886
1.126641540056258
0.866737862471463
0.663849792906007
Columns 9 through 12
1.453251190259060
elija el grado del polinomio5
O =
1.0e+005 *
0.000120000000000 0.000120000000000
-0.000000000000000 -0.000000000000000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
-0.000000000000000 -0.000000000000000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
1.353048857058631 1.353048857058631
bb =
1.0e+003 *
0.014571488505484 0.011202555950371 0.001293563545585 0.114539016576461 -0.128064107164516 1.002229547669045
sistema =
1.0e+005 *
0.000120000000000 0.000120000000000
-0.0000000000 -0.000000000000000 00000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.000145714885055 0.000145714885055
-0.000000000000000 -0.000000000000000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
0.000112025559504 0.000112025559504
0.000425454545455 0.000425454545455
-0.0000000000 -0.000000000000000 00000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.000012935635456 0.000012935635456
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
0.001145390165765 0.001145390165765
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
-0.001280641071645 -0.001280641071645
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
1.353048857058631 1.353048857058631
0.010022295476690 0.010022295476690
sol =
2.649071560543261 -0.951161669565782 -0.351650193548362 0.286206717849582 -0.008388002357245 -0.012621939549015
>> 1.0e+002 *
0.145714885054841 0.112025559503709 0.012935635455847 1.145390165764610 -1.280641071645164 ???
1.0e+002 * |
Error: Expression or statement is incomplete or incorrect.
>> ,c2 ??? Undefined function or variable 'c2'.
>> mc2 Elija los los
valores de xlinspace(-3,3,12) xlinspace(-3,3,12)
x =
Columns 1 through 8
-3.000000000000000 -3.000000000000000
-2.454545454545455 -2.454545454545455
-1.909090909090909 -1.909090909090909
-1.363636363636364 -1.363636363636364
1.909090909090909
2.454545454545454
3.000000000000000
-0.818181818181818 -0.818181818181818
-0.272727272727273 -0.272727272727273
0.272727272727273 0.272727272727273
0.818181818181818 0.818181818181818
2.993596785794432 2.993596785794432
2.733489951018636 2.733489951018636
2.297864622225752 2.297864622225752
1.849415392302503 1.849415392302503
Columns 9 through 12
1.363636363636363
Ingrese las parejas de los los datos de
x3*sin(exp(-x/2)) x3*sin(exp(-x/2))
y =
Columns 1 through 8
-2.920519778316971 -2.920519778316971
-0.801116507633982 -0.801116507633982
1.552952540062045 1.552952540062045
2.755325114338886 2.755325114338886
1.126641540056258
0.866737862471463
0.663849792906007
Columns 9 through 12
1.453251190259060
elija el grado del polinomio5
O =
1.0e+005 *
0.000120000000000 0.000120000000000
-0.000000000000000 -0.000000000000000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
-0.000000000000000 -0.000000000000000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
1.353048857058631 1.353048857058631
bb =
1.0e+003 *
0.014571488505484 0.011202555950371 0.001293563545585 0.114539016576461 -0.128064107164516 1.002229547669045
sistema =
1.0e+005 *
0.000120000000000 0.000120000000000
-0.0000000000 -0.000000000000000 00000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.000145714885055 0.000145714885055
-0.000000000000000 -0.000000000000000
0.000425454545455 0.000425454545455
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
0.000112025559504 0.000112025559504
0.000425454545455 0.000425454545455
-0.0000000000 -0.000000000000000 00000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.000012935635456 0.000012935635456
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
0.001145390165765 0.001145390165765
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
-0.001280641071645 -0.001280641071645
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
-0.000000000000000 -0.000000000000000
1.353048857058631 1.353048857058631
0.010022295476690 0.010022295476690
3.036003631973320 3.036003631973320
2.876490281431784 2.876490281431784
2.369248428895213 2.369248428895213
1.783817348489831 1.783817348489831
3.036003631973320 3.036003631973320
2.876490281431784 2.876490281431784
2.369248428895213 2.369248428895213
1.783817348489831 1.783817348489831
sol =
2.649071560543261 -0.951161669565782 -0.351650193548362 0.286206717849582 -0.008388002357245 -0.012621939549015
>> sol(1)+ x*sol(2) +sol(3)*x.^2 +sol(4)*x.^3 +sol(5)*x.^4 +sol(6)*x.^5
ans =
Columns 1 through 8
-3.002173435159545 -3.002173435159545
-0.547252376457052 -0.547252376457052
1.400546187945299 1.400546187945299
2.596994743133328 2.596994743133328
1.111487642194758
0.999218285133998
0.611756690501803
Columns 9 through 12
1.335351077401359
>> y2 =sol(1)+ x*sol(2) +sol(3)*x.^2 +sol(4)*x.^3 +sol(5)*x.^4 +sol(5)*x.^4 +sol(6)*x.^5
y2 =
Columns 1 through 8
-3.002173435159545 -3.002173435159545
-0.547252376457052 -0.547252376457052
1.400546187945299 1.400546187945299
2.596994743133328 2.596994743133328
Columns 9 through 12
1.335351077401359
1.111487642194758
0.999218285133998
0.611756690501803
>> plot(x,y,'og') plot(x,y,'og') >> hold on >> plot(x,y2,'m') plot(x,y2,'m') >> gtext('-------Ajuste gtext('-------Ajuste de polinimio polinimio
grado 5-------------') 5-------------')
>> sx
sx =
1.0e+005 *
Columns 1 through 8
-0.000000000000000 -0.000000000000000
0.000425454545455 0.000425454545455
Columns 9 through 10
-0.000000000000000
>> sx'
ans =
1.0e+005 *
-0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 1.353048857058631
>> b
b =
1.353048857058631
-0.000000000000000 -0.000000000000000
0.002689857250188 0.002689857250188
-0.000000000000000 -0.000000000000000
0.020056632246928 0.020056632246928
-0.000000000000000 -0.000000000000000
0.161343159651034 0.161343159651034
1.0e+003 *
0.014571488505484 0.014571488505484
0.011202555950371 0.011202555950371
0.001293563545585 0.001293563545585
0.114539016576461 0.114539016576461
-0.128064107164516 -0.128064107164516
1.002229547669045 1.002229547669045
-2.454545454545455 -2.454545454545455
-1.909090909090909 -1.909090909090909
-1.363636363636364 -1.363636363636364
-0.818181818181818 -0.818181818181818
-0.272727272727273 -0.272727272727273
0.272727272727273 0.272727272727273
0.818181818181818 0.818181818181818
1.909090909090909 1.909090909090909
2.454545454545454 2.454545454545454
3.000000000000000 3.000000000000000
-2.920519778316971 -2.920519778316971
-0.801116507633982 -0.801116507633982
1.552952540062045 1.552952540062045
2.755325114338886 2.755325114338886
2.297864622225752
1.849415392302503
1.453251190259060
1.126641540056258
0.866737862471463
0.663849792906007
1.400546187945299 1.400546187945299
2.596994743133328 2.596994743133328
3.036003631973320 3.036003631973320
2.876490281431784 2.876490281431784
2.369248428895213 2.369248428895213
1.783817348489831 1.783817348489831
0.999218285133998
0.611756690501803
>> b'
ans =
1.0e+003 *
0.014571488505484 0.011202555950371 0.001293563545585 0.114539016576461 -0.128064107164516 1.002229547669045
>> [x,y,y2]
ans =
Columns 1 through 8
-3.000000000000000 -3.000000000000000
Columns 9 through 16
1.363636363636363 1.363636363636363
Columns 17 through 24
2.993596785794432
2.733489951018636
Columns 25 through 32
-3.002173435159545 -3.002173435159545
-0.547252376457052 -0.547252376457052
Columns 33 through 36
1.335351077401359
>> [x;y;y2]'
1.111487642194758
ans =
-3.000000000000000 -2.920519778316971 -3.002173435159545 -2.454545454545455 -0.801116507633982 -0.547252376457052 -1.909090909090909
1.552952540062045
1.400546187945299
-1.363636363636364
2.755325114338886
2.596994743133328
-0.818181818181818
2.993596785794432
3.036003631973320
-0.272727272727273
2.733489951018636
2.876490281431784
0.272727272727273
2.297864622225752
2.369248428895213
0.818181818181818
1.849415392302503
1.783817348489831
1.363636363636363
1.453251190259060
1.335351077401359
1.909090909090909
1.126641540056258
1.111487642194758
2.454545454545454
0.866737862471463
0.999218285133998
3.000000000000000
0.663849792906007
0.611756690501803
