Durand-Kerner Root-Finding Method for the Generalized Tridiagonal Eigenproblem

TR-2002020: Inverse Power and Durand-Kerner Iterations for Univariate Polynomial Root-Finding

Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems

In this paper we consider the application of polynomial root-finding methods to the solution of the tridiagonal matrix eigenproblem. All considered solvers are based on evaluating the Newton correction. We show that the use of scaled three-term recurrence relations complemented with error free transformations yields some compensated schemes which significantly improve the accuracy of computed r...

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...

Generalized Probabilistic Bisection for Stochastic Root-Finding

We consider numerical schemes for root finding of noisy responses through generalizing the Probabilistic Bisection Algorithm (PBA) to the more practical context where the sampling distribution is unknown and location-dependent. As in standard PBA, we rely on a knowledge state for the approximate posterior of the root location. To implement the corresponding Bayesian updating, we also carry out ...

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 ...