A GENERALISED SPARSE FACTORISATION METHOD FOR THE SOLUTION OF THE GENERAL PERIODIC TRIDIAGONAL SYSTE

A GENERALISED SPARSE FACTORISATION METHOD FOR THE SOLUTION OF THE GENERAL PERIODIC TRIDIAGONAL SYSTE

Author by Dr. Samuel Okolie

Language: English

Abstract

Previously proposed factorisation methods for the solution of the general periodic tridiagonal matrix systems have not been entirely successful in maintaining the sparsity of the given coefficient matrix in the factorisation process. Here, a general sparse cyclic factorisation method involving a continued fraction expansion whilst maintaining both the sparsity and form of the 'given coefficient. matrix is proposed. The resulting algorithmic solution is shown to be a very fast method which is recommended for use in problems requiring a repeated solution of the matrix system as in the solution of the Crank-Nicolson finite difference equations derived from linear self-adjoint parabolic problems under periodic spatial boundary conditions.


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