solving a sequence in matlab

Ax1 = b, 
Ax2 = x1
Ax3 = x2, 
Ax4 = x3, 
Ax = x4,

how to solve this sequence A and b are defined

A = diag(2*ones(1,n)) - diag(ones(1,n-1),1) - diag(ones(1,n-1),-1)
b = [0:1:n/2-1 n/2-1:-1:0]’

[James Tursa]

Please explain in more detail. Does Ax1 mean A*x1, so that the line Ax1 = b means A*x1 = b and you are solving for x1? Then you use that to solve for x1, x3, x4, and ultimately x?

Answer 1

[James Tursa]

Plugging everything in I get

A^5 * x = b

So the solution would be

x = A^5 \ b

However, your expressions for A and b don't seem right since the dimensions are incompatible for the linear expression. E.g.,

>> n = 3
n =
     3
>> A = diag(2*ones(1,n)) - diag(ones(1,n-1),1) - diag(ones(1,n-1),-1)
A =
     2    -1     0
    -1     2    -1
     0    -1     2
>> b = [0:1:n/2-1 n/2-1:-1:0]'
b =
                   0
   0.500000000000000
>> A^5\b
Error using  \ 
Matrix dimensions must agree.

[HIGH]

Thanks for the reply. Actually A and b are correct and I figured the X's out. but I need to write a function for "upper bidiagonal system" to find these X'using the attached m files. I tried couple of ways but yet having trouble writing the function.

 Ohh I am sorry, n should be equal to 10.. n=10

[HIGH]

n=10 sorry