A Method of Solving a System of Linear Equations Whose Coefficients Form a Tridiagonal Matrix* By

A~1 so obtained, however, is no longer a tridiagonal matrix. If 1 is a n X ft matrix, we will have in general n2 elements of A-1. When n is large, this method becomes unwieldy, even with an electronic computer. Linear equations similar to Eqs. (1) are frequently encountered in problems of mathematical physics. For instance, the backward finite difference method for solving the heat equation requires the solution of equations (2) for each step where A is fixed and d is changed from step to step. Heat equations also appear in the study of longitudinal impact on visco-plastic rods. The solution of other problems, such as discretely loaded strings and the application of the three moment theorem to continuous beams, result in equations of the form of (2). Methods are known which enable one to determine x of (2) more efficiently than by using Eq. (3) (see [1], [2] for example). In the following, we will present another method which is very efficient and convenient for ordinary physical problems. The comparison with the traditional triangular decomposition method is presented in the Appendix.