The LUMPROVE function uses LU decomposition to iteratively improve an approximate solution X of a set of n linear equations in n unknowns Ax = b.

Note: If you are working with complex inputs, use the LA_LUMPROVE function instead.

## Examples

This example uses LUMPROVE to improve an approximate solution X to the linear system Ax = B:

; Create coefficient array A:
A = [[ 2.0,  1.0,  1.0], \$
[ 4.0, -6.0,  0.0], \$
[-2.0,  7.0,  2.0]]
; Create a duplicate of A:
alud = A
; Define the right-hand side vector B:
B = [3.0, -8.0, 10.0]
; Begin with an estimated solution X:
X = [.89, 1.78, -0.88]
; Decompose the duplicate of A:
LUDC, alud, INDEX
; Compute an improved solution:
result = LUMPROVE(A, alud, INDEX, B, X)
; Print the result:
PRINT, result

IDL prints:

1.00000 2.00000 -1.00000

This is the exact solution vector.

## Syntax

Result = LUMPROVE( A, Alud, Index, B, X [, /COLUMN] [, /DOUBLE] )

## Return Value

The result is a vector, whose type and length are identical to X, containing the improved solution.

## Arguments

### A

The n by n coefficient array of the linear system Ax = b.

### Alud

The n by n LU decomposition of A created by the LUDC procedure.

### Index

An input vector, created by the LUDC procedure, containing a record of the row permutations which occurred as a result of partial pivoting.

### B

An n-element vector containing the right-hand side of the linear system
Ax = b.

### X

An n-element vector containing the approximate solution of the linear system
Ax = b.

## Keywords

### COLUMN

Set this keyword if the input array A is in column-major format (composed of column vectors) rather than in row-major format (composed of row vectors).

### DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

## Version History

 4 Introduced

## Resources and References

LUMPROVE is based on the routine mprove described in section 2.5 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.