12. Linear Algebra

This chapter describes functions for solving linear systems. The library provides simple linear algebra operations which operate directly on the gsl_vector and gsl_matrix objects. These are intended for use with "small" systems where simple algorithms are acceptable.

Anyone interested in large systems will want to use the sophisticated routines found in LAPACK. The Fortran version of LAPACK is recommended as the standard package for linear algebra. It supports blocked algorithms, specialized data representations and other optimizations.

The functions described in this chapter are declared in the header file `gsl_linalg.h'.

12.1 LU Decomposition
12.2 QR Decomposition
12.3 QR Decomposition with Column Pivoting
12.4 Singular Value Decomposition
12.5 Cholesky Decomposition
12.6 Tridiagonal Decomposition of Real Symmetric Matrices
12.7 Tridiagonal Decomposition of Hermitian Matrices
12.8 Bidiagonalization
12.9 Householder solver for linear systems
12.10 Tridiagonal Systems
12.11 Examples
12.12 References and Further Reading