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Home/Magazine Archive/April 1969 (Vol. 12, No. 4)/An algorithm for solving a special class of tridiagonal.../Abstract

An algorithm for solving a special class of tridiagonal systems of linear equations

By Donald J. Rose
Communications of the ACM, April 1969, Vol. 12 No. 4, Pages 234-236
10.1145/362912.362940
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An algorithm is presented for solving a system of linear equations Bu = k where B is tridiagonal and of a special form. This form arises when discretizing the equation - d/dx (p(x) du/dx) = k(x) (with appropriate boundary conditions) using central differences. It is shown that this algorithm is almost twice as fast as the Gaussian elimination method usually suggested for solving such systems. In addition, explicit formulas for the inverse and determinant of the matrix B are given.

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