
A Provably Componentwise Backward Stable O(n^2) QR Algorithm for the Diagonalization of Colleague Matrices
The roots of a monic polynomial expressed in a Chebyshev basis are known...
read it

Derivatives of partial eigendecomposition of a real symmetric matrix for degenerate cases
This paper presents the forward and backward derivatives of partial eige...
read it

Poleswapping algorithms for alternating and palindromic eigenvalue problems
Poleswapping algorithms are generalizations of bulgechasing algorithms...
read it

GCGE: A Package for Solving Large Scale Eigenvalue Problems by Parallel Block Damping Inverse Power Method
We propose an eigensolver and the corresponding package, GCGE, for solvi...
read it

Stable Backward Diffusion Models that Minimise Convex Energies
Backward diffusion processes appear naturally in image enhancement and d...
read it

Backward Error Measures for Roots of Polynomials
We analyze different measures for the backward error of a set of numeric...
read it

Backward CUSUM for Testing and Monitoring Structural Change
It is well known that the conventional CUSUM test suffers from low power...
read it
Backward Stability of Explicit External Deflation for the Symmetric Eigenvalue Problem
A thorough backward stability analysis of Hotelling's deflation, an explicit external deflation procedure through lowrank updates for computing many eigenpairs of a symmetric matrix, is presented. Computable upper bounds of the loss of the orthogonality of the computed eigenvectors and the symmetric backward error norm of the computed eigenpairs are derived. Sufficient conditions for the backward stability of the explicit external deflation procedure are revealed. Based on these theoretical results, the strategy for achieving numerical backward stability by dynamically selecting the shifts is proposed. Numerical results are presented to corroborate the theoretical analysis and to demonstrate the stability of the procedure for computing many eigenpairs of large symmetric matrices arising from applications.
READ FULL TEXT
Comments
There are no comments yet.