Regresion Polinomial Con Matlab

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 4Tabla 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)

x =

Columns 1 through 8

-3.000000000000000 -2.454545454545455 -1.909090909090909 -1.363636363636364 -0.818181818181818 -0.272727272727273 0.272727272727273 0.818181818181818

Columns 9 through 12

1.363636363636363 1.909090909090909 2.454545454545454 3.000000000000000

Ingrese las parejas de los datos de x3*sin (exp(-x/2))

y =

Columns 1 through 8

-2.920519778316971 -0.801116507633982 1.552952540062045 2.755325114338886 2.993596785794432 2.733489951018636 2.297864622225752 1.849415392302503

Columns 9 through 12

1.453251190259060 1.126641540056258 0.866737862471463 0.663849792906007

elija el grado del polinomio4

O =

1.0e+004 *

0.001200000000000 -0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878

-0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000

0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280

-0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000

0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000 1.613431596510340

bb =

1.0e+002 *

0.145714885054841

0.112025559503709

0.012935635455847

1.145390165764610

-1.280641071645164

sistema =

Sistema de ecuaciones

1.0e+004 *

0.001200000000000 -0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878 0.001457148850548

-0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000 0.001120255595037

0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280 0.000129356354558

-0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000 0.011453901657646

0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000 1.613431596510340 -0.012806410716452

Solucion

sol =

2.649071560543259

-0.642661673276221

-0.351650193548361

0.143297154360733

-0.008388002357245

Polinomio

2.649071560543259 + -0.642661673276221*x + -0.351650193548361*x.^2 + 0.143297154360733*x.^3 + -0.008388002357245*x.^4

Sumatorias de x

sx'

ans =

1.0e+004 *

-0.000000000000000 x.^1

0.004254545454545 x.^2

-0.000000000000000 x.^3

0.026898572501878 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)

x =

Columns 1 through 8

-3.000000000000000 -2.454545454545455 -1.909090909090909 -1.363636363636364 -0.818181818181818 -0.272727272727273 0.272727272727273 0.818181818181818

Columns 9 through 12

1.363636363636363 1.909090909090909 2.454545454545454 3.000000000000000

Ingrese las parejas de los datos de x3*sin(exp(-x/2))

y =

Columns 1 through 8

-2.920519778316971 -0.801116507633982 1.552952540062045 2.755325114338886 2.993596785794432 2.733489951018636 2.297864622225752 1.849415392302503

Columns 9 through 12

1.453251190259060 1.126641540056258 0.866737862471463 0.663849792906007

elija el grado del polinomio5

O =

1.0e+005 *

0.000120000000000 -0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000

-0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928

0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000

-0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034

0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000

-0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 1.353048857058631

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 -0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.000145714885055

-0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 0.000112025559504

0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.000012935635456

-0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 0.001145390165765

0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 -0.001280641071645

-0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 1.353048857058631 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 -0.951161669565782x -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 x.^6

-0.000000000000000 x.^7

0.161343159651034 x.^8

-0.000000000000000 x.^9

1.353048857058631 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 desde le termino independiente hasta x ... 1 x x.^2% x.^3 etc clear,x=input('Elija los valores de x')A= length(x);y=input('Ingrese las parejas de los datos de x')m=input('elija el grado del polinomio');gms=m*2; % es el grado maximo de la sumatoriaif 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); endbb=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 endB=sx; % es el vector de sumatorias de x grado nfor 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); endbb=b'sistema=[O bb]sol=O\bbend%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 normal son los valores tabulados%r =sqrt((t1-t2)./t1)*100; %fprintf('\nr porcentual de orden 5 = %8.2f\n',r)

%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 VARIABLES ASIGNADASb 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 INTACTO

x=linspace(-3,3,12)

x =

Columns 1 through 8

-3.000000000000000 -2.454545454545455 -1.909090909090909 -1.363636363636364 -0.818181818181818 -0.272727272727273 0.272727272727273 0.818181818181818

Columns 9 through 12

1.363636363636363 1.909090909090909 2.454545454545454 3.000000000000000

>> y = 3*sin(exp(-x/2))

y =

Columns 1 through 8

-2.920519778316971 -0.801116507633982 1.552952540062045 2.755325114338886 2.993596785794432 2.733489951018636 2.297864622225752 1.849415392302503

Columns 9 through 12

1.453251190259060 1.126641540056258 0.866737862471463 0.663849792906007

>> format long

>> mc2

Elija los valores de xlinspace(-3,3,12)

x =

Columns 1 through 8

-3.000000000000000 -2.454545454545455 -1.909090909090909 -1.363636363636364 -0.818181818181818 -0.272727272727273 0.272727272727273 0.818181818181818

Columns 9 through 12

1.363636363636363 1.909090909090909 2.454545454545454 3.000000000000000

Ingrese las parejas de los datos de x3*sin(exp(-x/2))

y =

Columns 1 through 8

-2.920519778316971 -0.801116507633982 1.552952540062045 2.755325114338886 2.993596785794432 2.733489951018636 2.297864622225752 1.849415392302503

Columns 9 through 12

1.453251190259060 1.126641540056258 0.866737862471463 0.663849792906007

elija el grado del polinomio4

O =

12 * 468/11 * 18829/70

* 468/11 * 18829/70 *

468/11 * 18829/70 * 196555/98

* 18829/70 * 196555/98 *

18829/70 * 196555/98 * 306552/19

bb =

34753/2385

6139/548

824/637

16150/141

-9989/78

sistema =

12 * 468/11 * 18829/70 34753/2385

* 468/11 * 18829/70 * 6139/548

468/11 * 18829/70 * 196555/98 824/637

* 18829/70 * 196555/98 * 16150/141

18829/70 * 196555/98 * 306552/19 -9989/78

sol =

2710/1023

-705/1097

-2099/5969

977/6818

-78/9299

Elija los valores de xlinspace(-3,3,12)

x =

Columns 1 through 10

-3 -27/11 -21/11 -15/11 -9/11 -3/11 3/11 9/11 15/11 21/11

Columns 11 through 12

27/11 3

Ingrese las parejas de los datos de x3*sin (exp(-x/2))

y =

Columns 1 through 10

-2021/692 -1148/1433 1657/1067 4786/1737 2805/937 1159/424 6349/2763 1265/684 715/492 1201/1066

Columns 11 through 12

813/938 707/1065

elija el grado del polinomio4

O =

12 * 468/11 * 18829/70

* 468/11 * 18829/70 *

468/11 * 18829/70 * 196555/98

* 18829/70 * 196555/98 *

18829/70 * 196555/98 * 306552/19

bb =

34753/2385

6139/548

824/637

16150/141

-9989/78

sistema =

12 * 468/11 * 18829/70 34753/2385

* 468/11 * 18829/70 * 6139/548

468/11 * 18829/70 * 196555/98 824/637

* 18829/70 * 196555/98 * 16150/141

18829/70 * 196555/98 * 306552/19 -9989/78

sol =

2710/1023

-705/1097

-2099/5969

977/6818

-78/9299

>> format long

>> mc2

Elija los valores de xlinspace(-3,3,12)

x =

Columns 1 through 8

-3.000000000000000 -2.454545454545455 -1.909090909090909 -1.363636363636364 -0.818181818181818 -0.272727272727273 0.272727272727273 0.818181818181818

Columns 9 through 12

1.363636363636363 1.909090909090909 2.454545454545454 3.000000000000000

Ingrese las parejas de los datos de x3*sin (exp(-x/2))

y =

Columns 1 through 8

-2.920519778316971 -0.801116507633982 1.552952540062045 2.755325114338886 2.993596785794432 2.733489951018636 2.297864622225752 1.849415392302503

Columns 9 through 12

1.453251190259060 1.126641540056258 0.866737862471463 0.663849792906007

elija el grado del polinomio4

O =

1.0e+004 *

0.001200000000000 -0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878

-0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000

0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280

-0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000

0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000 1.613431596510340

bb =

1.0e+002 *

0.145714885054841

0.112025559503709

0.012935635455847

1.145390165764610

-1.280641071645164

sistema =

1.0e+004 *

0.001200000000000 -0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878 0.001457148850548

-0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000 0.001120255595037

0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280 0.000129356354558

-0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000 0.011453901657646

0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000 1.613431596510340 -0.012806410716452

sol =

2.649071560543259

-0.642661673276221

-0.351650193548361

0.143297154360733

-0.008388002357245

>> 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 -0.315671593136276 1.485865423905590 2.479172941092940 2.857239518532725 2.795233866231512 2.450504844095480 1.962581461930424

Columns 9 through 12

1.453172879441748 1.026168406234469 0.767637501813223 0.745829775582253

>> hold on

>> plot(x,y1,'r')

>> 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]'

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

>> sx

sx =

1.0e+004 *

-0.000000000000000 0.004254545454545 -0.000000000000000 0.026898572501878 -0.000000000000000 0.200566322469280 -0.000000000000000 1.613431596510340

>> format rational

>> sx

sx =

* 468/11 * 18829/70 * 196555/98 * 306552/19

>> sx'

ans =

-1/562949953421312

468/11

-1/140737488355328

18829/70

-1/17592186044416

196555/98

-1/1099511627776

306552/19

>> 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 0.112025559503709 0.012935635455847 1.145390165764610 -1.280641071645164

>> b'

ans =

1.0e+002 *

0.145714885054841

0.112025559503709

0.012935635455847

1.145390165764610

-1.280641071645164

Elija los valores de xlinspace(-3,3,12)

x =

Columns 1 through 8

-3.000000000000000 -2.454545454545455 -1.909090909090909 -1.363636363636364 -0.818181818181818 -0.272727272727273 0.272727272727273 0.818181818181818

Columns 9 through 12

1.363636363636363 1.909090909090909 2.454545454545454 3.000000000000000

Ingrese las parejas de los datos de x3*sin(exp(-x/2))

y =

Columns 1 through 8

-2.920519778316971 -0.801116507633982 1.552952540062045 2.755325114338886 2.993596785794432 2.733489951018636 2.297864622225752 1.849415392302503

Columns 9 through 12

1.453251190259060 1.126641540056258 0.866737862471463 0.663849792906007

elija el grado del polinomio5

O =

1.0e+005 *

0.000120000000000 -0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000

-0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928

0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000

-0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034

0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000

-0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 1.353048857058631

bb =

1.0e+003 *

0.014571488505484

0.011202555950371

0.001293563545585

0.114539016576461

-0.128064107164516

1.002229547669045

sistema =

1.0e+005 *

0.000120000000000 -0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.000145714885055

-0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 0.000112025559504

0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.000012935635456

-0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 0.001145390165765

0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 -0.001280641071645

-0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 1.353048857058631 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 valores de xlinspace(-3,3,12)

x =

Columns 1 through 8

-3.000000000000000 -2.454545454545455 -1.909090909090909 -1.363636363636364 -0.818181818181818 -0.272727272727273 0.272727272727273 0.818181818181818

Columns 9 through 12

1.363636363636363 1.909090909090909 2.454545454545454 3.000000000000000

Ingrese las parejas de los datos de x3*sin(exp(-x/2))

y =

Columns 1 through 8

-2.920519778316971 -0.801116507633982 1.552952540062045 2.755325114338886 2.993596785794432 2.733489951018636 2.297864622225752 1.849415392302503

Columns 9 through 12

1.453251190259060 1.126641540056258 0.866737862471463 0.663849792906007

elija el grado del polinomio5

O =

1.0e+005 *

0.000120000000000 -0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000

-0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928

0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000

-0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034

0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000

-0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 1.353048857058631

bb =

1.0e+003 *

0.014571488505484

0.011202555950371

0.001293563545585

0.114539016576461

-0.128064107164516

1.002229547669045

sistema =

1.0e+005 *

0.000120000000000 -0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.000145714885055

-0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 0.000112025559504

0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.000012935635456

-0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 0.001145390165765

0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 -0.001280641071645

-0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034 -0.000000000000000 1.353048857058631 0.010022295476690

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 -0.547252376457052 1.400546187945299 2.596994743133328 3.036003631973320 2.876490281431784 2.369248428895213 1.783817348489831

Columns 9 through 12

1.335351077401359 1.111487642194758 0.999218285133998 0.611756690501803

>> y2 =sol(1)+ x*sol(2) +sol(3)*x.^2 +sol(4)*x.^3 +sol(5)*x.^4 +sol(6)*x.^5

y2 =

Columns 1 through 8

-3.002173435159545 -0.547252376457052 1.400546187945299 2.596994743133328 3.036003631973320 2.876490281431784 2.369248428895213 1.783817348489831

Columns 9 through 12

1.335351077401359 1.111487642194758 0.999218285133998 0.611756690501803

>> plot(x,y,'og')

>> hold on

>> plot(x,y2,'m')

>> gtext('-------Ajuste de polinimio grado 5-------------')

>> sx

sx =

1.0e+005 *

Columns 1 through 8

-0.000000000000000 0.000425454545455 -0.000000000000000 0.002689857250188 -0.000000000000000 0.020056632246928 -0.000000000000000 0.161343159651034

Columns 9 through 10

-0.000000000000000 1.353048857058631

>> 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 =

1.0e+003 *

0.014571488505484 0.011202555950371 0.001293563545585 0.114539016576461 -0.128064107164516 1.002229547669045

>> 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 -2.454545454545455 -1.909090909090909 -1.363636363636364 -0.818181818181818 -0.272727272727273 0.272727272727273 0.818181818181818

Columns 9 through 16

1.363636363636363 1.909090909090909 2.454545454545454 3.000000000000000 -2.920519778316971 -0.801116507633982 1.552952540062045 2.755325114338886

Columns 17 through 24

2.993596785794432 2.733489951018636 2.297864622225752 1.849415392302503 1.453251190259060 1.126641540056258 0.866737862471463 0.663849792906007

Columns 25 through 32

-3.002173435159545 -0.547252376457052 1.400546187945299 2.596994743133328 3.036003631973320 2.876490281431784 2.369248428895213 1.783817348489831

Columns 33 through 36

1.335351077401359 1.111487642194758 0.999218285133998 0.611756690501803

>> [x;y;y2]'

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