Accurate computation of singular values and eigenvalues of symmetric matrices

We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the highest possible relative accuracy

Relative perturbation of invariant subspaces

In this paper we consider the upper bound for the sine of the greatest canonical angle between the original invariant subspace and its perturbation. We present our recent results which generalize some of the results from the relative perturbation theory of indefinite Hermitian matrices

A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU--GPU parallelism are discussed.Comment: Accepted for publication in BIT Numerical Mathematic

Novel Modifications of Parallel Jacobi Algorithms

We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other eigenvalue algorithms. If the matrices permit, both types of algorithms compute the eigenvalues and eigenvectors with high relative accuracy. We present novel parallelization techniques for both trigonometric and hyperbolic classes of algorithms, as well as some new ideas on how pivoting in each cycle of the algorithm can improve the speed of the parallel one-sided algorithms. These parallelization approaches are applicable to both distributed-memory and shared-memory machines. The numerical testing performed indicates that the hyperbolic algorithms may be superior to the trigonometric ones, although, in theory, the latter seem more natural.Comment: Accepted for publication in Numerical Algorithm

Accurate computation of singular values and eigenvalues of symmetric matrices

We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the highest possible relative accuracy

Can oversight mitigate auditor's motivated reasoning? An experimental study

Evidence of auditors’ failure to provide an independent opinion has reopened debates on measures to ensure auditor independence. We examine the effectiveness of oversight on two prominent determinants of auditor’s biased opinion – financial incentives and a personal relationship with the client. We conduct a between-subject experiment involving an accounting choice task. We find a significant effect of a personal relationship on the auditor’s choice after controlling for financial incentives. Oversight has a significant negative effect on auditor’s choice arising from financial incentives, whereas a personal relationship significantly reduces the effectiveness of oversight. Our results show that, in addition to oversight, other solutions that break up personal ties are needed to ensure auditor independence