SVBKSB Procedure

Uses "back substitution" to solve the set of simultaneous linear equations Ax = b, given the u, w, and v arrays created by the SVD procedure from the matrix a.

SVBKSB, u, w, v, b, x

u The m-by-n column matrix of the decomposition of a, as returned by SVD.

w The vector of singular values, as returned by SVD.

v The n-by-n orthogonal matrix of the decomposition of A, as returned by SVD.

b The vector containing the right-hand side of the equation.

x A variable containing the result.

None.

Since no input quantities are destroyed, SVBKSB may be called numerous times with different b vectors.

Here's a typical use of SVD and SVBKSB to solve the system Ax = b:

SVD, A, w, u, v

; Decompose square matrix A.

small = WHERE(w LT MAX(w) * 1.0e-6, count)

; Get subscripts of singular values, using a given threshold. 

IF count NE 0 THEN w(small) = 0.0

; Zero singular values less than the threshold. See the Numerical

; Recipes book (referred to in the See Also section) for details.

SVBKSB, u, w, v, b, x 

; The vector x now contains the solution.

PRINT, TOTAL(ABS(A # x - b))

; The residual, |Ax - b| should be near 0.

SVD

SVBKSB is based on the routine of the same name in Numerical Recipes in C: The Art of Scientific Computing, by Flannery, Press, Teukolsky, and Vetterling, Cambridge University Press, Cambridge, MA, 1988. It is used by permission.