Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix

The Lanczos algorithm for tridiagonalizing a symmetric matrixis the basis for several methods for solving sets of linearequations as well as for solving the eigenproblem. These methodsare very useful when the matrix is large and sparse. A completerounding error analysis of the algorithm is presented here,giving among other results an important expression for the lossof orthogonality of the computed vectors. The results here canbe used to analyze the many methods which are basedon the Lanczosalgorithm.