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Non‐iterative solution of a tridiagonal‐type matrix coupled by diagonal submatrices
Author(s) -
Deshpande M. D.
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200208
Subject(s) - tridiagonal matrix , block matrix , mathematics , recursion (computer science) , diagonal , matrix (chemical analysis) , algebraic equation , matrix splitting , band matrix , iterative method , recurrence relation , tridiagonal matrix algorithm , algebra over a field , algorithm , mathematical analysis , square matrix , pure mathematics , symmetric matrix , eigenvalues and eigenvectors , geometry , physics , nonlinear system , quantum mechanics , materials science , composite material
A non‐iterative method is presented for solving a system of algebraic equations forming a banded matrix with each diagonal submatrix being tridiagonal and all other submatrices being diagonal. A recursion relation is assumed between successive elements of the solution vector. This relation is determined by equating a linearly combined form of it with the original set of equations also being linearly combined. The solution vector is determined by back‐substitution of elements in the recursion relation. Since the method takes advantage of the banded structure of the matrix, it is more efficient than the conventional methods. A FORTRAN program that incorporates the present method is included.