Параллельные вычисления в ИММ УрО РАН
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Next: QR Factorization Up: Computational Routines Previous: Linear Equations
Orthogonal Factorizations and Linear Least Squares ProblemsScaLAPACK 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 ;
a complex matrix Q is unitary if .
Orthogonal or unitary matrices have the important property that they leave the
two-norm of a vector invariant:
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 |