Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
The Mathematica book (4th edition)
The Mathematica book (4th edition)
Multigrid
Using computer algebra systems in the development of scientific computer codes
Future Generation Computer Systems - Special section: Selected papers from the TERENA networking conference 2002
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For tridiagonal matrix systems, a simple direct algorithm giving the solution exists, but in the most general case of tridiagonal matrix with fringes, the direct solving algorithms are more complicated. For big systems, direct methods are not well fitted and iterative algorithms are preferable. In this paper a relaxation type iterative algorithm is presented. It is an extension of the backward substitution method used for simple tridiagonal matrix systems. The performances show that this algorithm is a good compromise between a direct method and other iterative methods as block SOR. Its nature suggests its use as inner solver in the solution of problems derived by application of a decomposition domain method. A special emphasis is done on the programming aspect. The solving Fortran subroutines implementing the algorithm have been generated automatically from their specification by using a computer algebra system technique.