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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_inline1183 ; a complex matrix Q is unitary if tex2html_wrap_inline1187 . 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.

Susan Blackford
Thu Jul 25 15:38:00 EDT 1996