Calculo numerico

Universidade Federal de Santa Maria
Centro de Educação Superior Norte-RS
Trabalho de Cálculo Numérico

2. -->A=[0.28 0.10 0.15; 0.12 0.22 0.10; 0.14 0.12 0.18]
A = 0.28 0.1 0.15 0.12 0.22 0.1 0.14 0.12 0.18 -->B=[20; 10; 12] B = 20. 10. 12. -->[l u p] = lu(A) p = 1. 0. 0. 0. 1. 0. 0. 0. 1. u = 0.28 0.1 0.15 0. 0.1771429 0.0357143 0. 0. 0.0908871 l = 1. 0. 0. 0.4285714 1. 0. 0.5 0.3951613 1. -->y = l\(p*B) y = 20. 1.4285714 1.4354839 -->x = u\y x = 61.22449 4.880213 15.794144

3. a)

b) -->function [raiz,iter]=bissec3(f,a,b,eps1),
-->x0=a;
-->x1=b;
-->xm=(x0+x1)./2;
-->it=0;
-->while ((x1-x0)>eps1)&it<=150 do
--> if f(x0).*f(xm) > 0 then
--> x0=xm; else x1=xm; end;
-->xm=(x0+x1)./2;
-->it=it+1;
-->end;
-->raiz=xm;
-->iter=it;
-->endfunction; -->function y=f(x), y=3*cos(x)-%e^(-0.4*x); endfunction;
Aviso: redefinindo a função: f
-->[raiz, iter] = bissec3(f,-2,0,0.001) iter = 11. raiz = - 1.0405273
3c)

4. a)

b) algsys([log(x)-y,2*x-4-y], [x,y]); load("mnewton"); mnewton([log(x)-y,2*x-4-y],[x,y],[1,1]); algsys: tried and failed to reduce system to a polynomial in one variable; give up. -- an error. (%o8)
"C:/PROGRA~1/MAXIMA~1.0-2/share/maxima/5.28.0-2/share/mnewton/mnewton.mac"
(%o9) [[x=2.447542160637616,y=0.89508432127523]]

(fpprec : 1, newtonepsilon : float(10^(-fpprec))); mnewton([log(x)-y, 2*x-4-y],[x,y],[1,1]);
(%o10) 0.1
(%o11)