Tridiagonal matrix

Summary

A tridiagonal matrix is a square matrix whose nonzero entries lie only on the main diagonal and on the two diagonals next to it. It is a band matrix of bandwidth one on each side, and it is both upper and lower Hessenberg. Linear systems with a tridiagonal matrix can be solved with a number of operations proportional to the size, not to its cube. Such matrices arise from finite difference schemes, from three-term recurrences and from the reduction of symmetric matrices for eigenvalue computations.