Homotopy Method for the Singular Symmetric Tridiagonal Eigenproblem

Parallel Bisection Algorithms for Solving the Symmetric Tridiagonal Eigenproblem

In this paper we study the different approaches used so far to apply the bisection method for solving the symmetric tridiagonal eigenproblem. We review the sequential methods used to perform the final extraction of the eigenvalues and compare two new techniques that offer very good results. The sequential version of the bisection method we have implemented even surpasses the results of the QR i...

On MR3-type Algorithms for the Tridiagonal Symmetric Eigenproblem and the Bidiagonal SVD

Iterative Methods for the Partial Symmetric Eigenproblem

Computing the Bidiagonal SVD Through an Associated Tridiagonal Eigenproblem

In this paper, we present an algorithm for the singular value decomposition (SVD) of a bidiagonal matrix by means of the eigenpairs of an associated symmetric tridiagonal matrix. The algorithm is particularly suited for the computation of a subset of singular values and corresponding vectors. We focus on a sequential implementation, discuss special cases and other issues. We use a large set of ...

Accuracy of the s-Step Lanczos Method for the Symmetric Eigenproblem in Finite Precision

The s-step Lanczos method is an attractive alternative to the classical Lanczos method as it enables an O(s) reduction in data movement over a fixed number of iterations. This can significantly improve performance on modern computers. In order for s-step methods to be widely adopted, it is important to better understand their error properties. Although the s-step Lanczos method is equivalent to...