In this paper we present an O(nk) procedure, Algorithm MR3, for computing k eigenvectors of an nÃ— n symmetric tridiagonal matrix T . A salient feature of the algorithm is that a number of differentâ€¦ (More)

This paper presents and analyzes a new algorithm for computing eigenvectors of symmetric tridiagonal matrices factored as LDLt, with D diagonal and L unit bidiagonal. If an eigenpair is well behavedâ€¦ (More)

We compare four algorithms from the latest LAPACK 3.1 release for computing eigenpairs of a symmetric tridiagonal matrix. These include QR iteration, bisection and inverse iteration (BI), theâ€¦ (More)

In the 1990's, Dhillon and Parlett devised the algorithm of multiple relatively robust representations (MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrixâ€¦ (More)

Suppose that one knows a very accurate approximation (+ to an eigenvalue A of a symmetric tridiagonal matrix T. A good way to approximate the eigenvector x is to discard an appropriate equation, sayâ€¦ (More)

IEEE Transactions on Visualization and Computerâ€¦

2005

This paper addresses several issues related to topological analysis of 3D second order symmetric tensor fields. First, we show that the degenerate features in such data sets form stable topologicalâ€¦ (More)

LAPACK is often mentioned as a positive example of a software library that encapsulates complex, robust, and widely used numerical algorithms for a wide range of applications. At installation time,â€¦ (More)

Let LDLt be the triangular factorization of an unreduced symmetric tridiagonal matrix T âˆ’ Ï„I . Small relative changes in the nontrivial entries of L and D may be represented by diagonal scalingâ€¦ (More)