ABSTRACT
When a large system of linear algebraic equations has a special pattern, such as a tridiagonal pattern, it is usually worthwhile to develop special methods for that unique pattern. There are a number of direct elimination methods for solving systems of linear algebraic equations which have special patterns in the coefficient matrix. These methods are generally very efficient in computer time and storage. Such methods should be considered when the coefficient matrix fits the required pattern, and when computer storage and/or execution time are important. One algorithm that deserves special attention is the algorithm for tridiagonal matrices, often referred to as the Thomas (1949) algorithm. Large tridiagonal systems arise naturally in a number of problems, especially in the numerical solution of differential equations by implicit methods. Consequently, the Thomas algorithm has found a large number of applications.
