| Functionality
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The software package PROPACK contains a set of functions for
solving the symmetric eigenvalue problem and for computing the
singular value decomposition of large and sparse or structured
matrices. The eigenvalue routines are based on the symmetric Lanczos
algorithm (PRO) with partial reorthogonalization, while the SVD
routines are based on the Lanczos bidiagonalization with partial
reorthogonalization (BPRO). The Lanczos routines can also be used
directly, and form the basis of efficient algorithms for solving
discrete ill-posed problems and linear systems of equations or linear
least squares problems with multiple right-hand sides (see e.g. the
technical report below and the thesis Efficient Algorithms
for helioseismic inversion. by RML).
The implementation of PRO is inspired by the FORTRAN 77 code found in
the LANSO package by Parlett, Simon and Wu (see e.g. Simon & Wu 1997). The
BPRO implementation is based on the algorithm described in
Rasmus Munk Larsen, "Lanczos bidiagonalization with
partial reorthogonalization for large sparse SVD and linear least squares
calculations", Tech. Rep., Computer Science Department, Aarhus
University, August 1998.
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