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Orthogonal Factorizations and Linear Least Squares Problems


ScaLAPACK provides a number of routines for factorizing a general rectangular m-by-n matrix A, as the product of an orthogonal matrix (unitary if complex) and a triangular (or possibly trapezoidal) matrix.  

A real matrix Q is orthogonal if tex2html_wrap_inline13210 ; a complex matrix Q is unitary if tex2html_wrap_inline13214 . Orthogonal or unitary matrices   have the important property that they leave the two-norm of a vector invariant:
As a result, they help to maintain numerical stability because they do not   amplify rounding errors.

Orthogonal factorizations    are used in the solution of linear least squares problems . They may also be used to perform preliminary steps in the solution of eigenvalue or singular value problems.

Table 3.7 lists all routines provided by ScaLAPACK to perform orthogonal factorizations and the generation or pre- or post-multiplication of the matrix Q for each matrix type and storage scheme.

Susan Blackford
Tue May 13 09:21:01 EDT 1997