integrate(x*cos(x)^3,x,0,%pi);

A4: matrix(
 [2,-1,0,0], 
 [-1,2,-1,0], 
 [0,-1,2,-1], 
 [0,0,-1,2]
);

d:eigenvalues(A4);

v:create_list(4*sin(k*%pi/(2*(4+1)))^2,k,1,4);

bfloat([-(sqrt(5)-3)/2,(sqrt(5)+3)/2,-(sqrt(5)-5)/2,(sqrt(5)+5)/2]);

bfloat(v);

A5: matrix(
 [2,-1,0,0,0], 
 [-1,2,-1,0,0], 
 [0,-1,2,-1,0], 
 [0,0,-1,2,-1], 
 [0,0,0,-1,2]
);

eigenvalues(A5);

b:[-1,2,3,2,1];
I: matrix(
 [1,0,0,0,0], 
 [0,1,0,0,0], 
 [0,0,1,0,0], 
 [0,0,0,1,0], 
 [0,0,0,0,1]
);

v:[0,0,1,1,0]$for k:1 thru 100 do (v:1/2*((2*I-A5).v+b));

bfloat(A5.v-b);

kill(all);