Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix

The Lanczos algorithm for tridiagonalizing a symmetric matrix is the basis for several methods for solving sets of linear equations as well as for solving the eigenproblem. These methods are very useful when the matrix is large and sparse. A complete rounding error analysis of the algorithm is presented here, giving among other results an important expression for the loss of orthogonality of the computed vectors. The results here can be used to analyze the many methods which are basedon the Lanczos algorithm.