High Quality Content by WIKIPEDIA articles! In numerical linear algebra, the tridiagonal matrix algorithm (TDMA), also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. For such systems, the solution can be obtained in O(n) operations instead of O(n3) required by Gaussian elimination. A first sweep eliminates the ai's, and then an (abbreviated) backward substitution produces the solution. Example of such matrices commonly arise from the discretization of 1D Poisson equation (e.g., the 1D diffusion problem) and natural cubic spline interpolation. The following C99 function will solve a general tridiagonal system. Note that the index i here is zero based, in other words i = 0, 1, dots, n - 1 where n is the number of unknowns.

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