This chapter describes functions for solving linear systems.

Singular Value Decomposition
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 -- Function: int gsl_la_decomp_SV_impl (gsl_matrix * A, gsl_matrix * Q, gsl_vector * S, double TOLERANCE)

LU Decomposition
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 -- Function: int gsl_la_decomp_LU_impl (gsl_matrix * MATRIX, gsl_vector_int * PERMUTATION, int * SIGNUM)

 -- Function: int gsl_la_solve_LU_impl (const gsl_matrix * LU_MATRIX, const gsl_vector_int * PERMUTATION, const gsl_vector * RHS, gsl_vector * SOLUTION)

QR Decomposition
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 -- Function: int gsl_la_decomp_QR_impl (gsl_matrix * MATRIX, gsl_vector * RDIAG, gsl_vector_int * PERMUTATION, int * SIGNUM)

 -- Function: int gsl_la_solve_QR_impl (const gsl_matrix * QR_MATRIX, const gsl_vector * RDIAG, const gsl_vector_int * PERMUTATION, const gsl_vector * RHS, gsl_vector * SOLUTION)

 -- Function: int gsl_la_solve_HH_impl (gsl_matrix * MATRIX, gsl_vector * VEC)

Tridiagonal Systems
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 -- Function: int gsl_la_solve_symm_tridiag_impl (const gsl_vector * DIAG, const gsl_vector * OFFDIAG, const gsl_vector * RHS, gsl_vector * SOLUTION)

 -- Function: int gsl_la_solve_symm_cyc_tridiag_impl (const gsl_vector * DIAG, const gsl_vector * OFFDIAG, const gsl_vector * RHS, gsl_vector * SOLUTION)

References and Further Reading
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For further information on the algorithms described in this section consult the following book,

  G. H. Golub, C. F. Van Loan, Matrix Computations (3rd Ed, 1996), Johns Hopkins University Press, ISBN 0-8018-5414-8.