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# res_with_prec

computes the residual r = Ax-b with precision

### Syntax

[r,norm2_r] = res_with_prec(A, x, b)

### Arguments

- A
real or complex sparse matrix (m x n)

- x
column vector (n x 1) or matrix (n x p)

- b
column vector (m x 1) or matrix (m x p)

- r
column vector (m x 1) or matrix (m x p)

- norm2_r
scalar or vector (1 x p) when b is a m x p matrix

### Description

This function computes the residual of a linear system `r = Ax - b`

(together
with its 2-norm) with the additional precision provided on "Intel like"
FPU (80 bits in place of 64) if the compiler translate "long double" to
use it. Else one must get the same than using `A*x - b`

at the scilab level.
In both cases using `[r, nr] = res_with_prec(A,x,b)`

is
faster than `r = A*x - b`

(and faster than `r = A*x - b; nr = norm(r)`

).

When `p > 1`

, `norm2_r(i)`

is the 2-norm of the vector `r(:,i)`

.

### Examples

[A] = ReadHBSparse(SCI+"/modules/umfpack/demos/bcsstk24.rsa"); C_ptr = taucs_chfact(A); b = rand(size(A,1),1); x0 = taucs_chsolve(C_ptr, b); norm(A*x0 - b) norm(res_with_prec(A, x0, b))

### See also

- taucs_chsolve — solves a linear s.p.d. system A*X = B from Cholesky factors of the sparse A

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