GNU Scientific Library Reference Manual - Third Edition (v1.12)by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

## 13.13 Tridiagonal Systems

The functions described in this section efficiently solve symmetric,
non-symmetric and cyclic tridiagonal systems with minimal storage.
Note that the current implementations of these functions use a variant
of Cholesky decomposition, so the tridiagonal matrix must be positive
definite. For non-positive definite matrices, the functions return
the error code `GSL_ESING`

.

__Function:__int**gsl_linalg_solve_tridiag***(const gsl_vector **`diag`, const gsl_vector *`e`, const gsl_vector *`f`, const gsl_vector *`b`, gsl_vector *`x`)- This function solves the general N-by-N system A x =
b where
`A`is tridiagonal ( N >= 2). The super-diagonal and sub-diagonal vectors`e`and`f`must be one element shorter than the diagonal vector`diag`. The form of`A`for the 4-by-4 case is shown below,A = ( d_0 e_0 0 0 ) ( f_0 d_1 e_1 0 ) ( 0 f_1 d_2 e_2 ) ( 0 0 f_2 d_3 )

__Function:__int**gsl_linalg_solve_symm_tridiag***(const gsl_vector **`diag`, const gsl_vector *`e`, const gsl_vector *`b`, gsl_vector *`x`)- This function solves the general N-by-N system A x =
b where
`A`is symmetric tridiagonal ( N >= 2). The off-diagonal vector`e`must be one element shorter than the diagonal vector`diag`. The form of`A`for the 4-by-4 case is shown below,A = ( d_0 e_0 0 0 ) ( e_0 d_1 e_1 0 ) ( 0 e_1 d_2 e_2 ) ( 0 0 e_2 d_3 )

__Function:__int**gsl_linalg_solve_cyc_tridiag***(const gsl_vector **`diag`, const gsl_vector *`e`, const gsl_vector *`f`, const gsl_vector *`b`, gsl_vector *`x`)- This function solves the general N-by-N system A x =
b where
`A`is cyclic tridiagonal ( N >= 3). The cyclic super-diagonal and sub-diagonal vectors`e`and`f`must have the same number of elements as the diagonal vector`diag`. The form of`A`for the 4-by-4 case is shown below,A = ( d_0 e_0 0 f_3 ) ( f_0 d_1 e_1 0 ) ( 0 f_1 d_2 e_2 ) ( e_3 0 f_2 d_3 )

__Function:__int**gsl_linalg_solve_symm_cyc_tridiag***(const gsl_vector **`diag`, const gsl_vector *`e`, const gsl_vector *`b`, gsl_vector *`x`)- This function solves the general N-by-N system A x =
b where
`A`is symmetric cyclic tridiagonal ( N >= 3). The cyclic off-diagonal vector`e`must have the same number of elements as the diagonal vector`diag`. The form of`A`for the 4-by-4 case is shown below,A = ( d_0 e_0 0 e_3 ) ( e_0 d_1 e_1 0 ) ( 0 e_1 d_2 e_2 ) ( e_3 0 e_2 d_3 )

ISBN 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |