Eigentest is a package that produces real test matrices with known eigensystems. A test matrix, called an eigenmat, is generated in a factored form, in which the user can specify the eigenvalues and has some control over the condition of the eigenvalues and eigenvectors. An eigenmat A of order n requires only O ( n ) storage for its representation. Auxiliary programs permit the computation of ( A − sI ) b , ( A − sI ) T b , ( A − sI ) −1 b , and ( A − sI ) −T b in O ( n ) operations. A special routine computes specified eigenvectors of an eigenmat and the condition of its eigenvalue. Thus eigenmats are suitable for testing algorithms based on Krylov sequences, as well as others based on matrix-vector products. This article introduces the eigenmat and describes implementations in Fortran 77, Fortran 95, C, and Matlab.

In many applications---latent semantic indexing, for example---it is required to obtain a reduced rank approximation to a sparse matrix A . Unfortunately, the approximations based on traditional decompositions, like the singular value and QR decompositions, are not in general sparse. Stewart [(1999), 313--323] has shown how to use a variant of the classical Gram--Schmidt algorithm, called the quasi--Gram-Schmidt--algorithm, to obtain two kinds of low-rank approximations. The first, the SPQR, approximation, is a pivoted, Q-less QR approximation of the form ( XR 11 −1 )( R 11 R 12 ), where X consists of columns of A. The second, the SCR approximation, is of the form the form A ≅ XTY T , where X and Y consist of columns and rows A and T , is small. In this article we treat the computational details of these algorithms and describe a MATLAB implementation.

The rapid and widespread adoption of Java has created a demand for reliable and reusable mathematical software components to support the growing number of computationally intensive applications now under development, particularly in science and engineering. In this paper we address practical issues of the Java language and environment which have an effect on numerical library design and development. Benchmarks which illustrate the current levels of performance of key numerical kernels on a variety of Java platforms are presented. Finally, a strategy for the development of a fundamental numerical toolkit for Java is proposed and its current status is described. © 1998 John Wiley & Sons, Ltd.

SRRT is a Fortran program to calculate an approximate orthonomral basis fr a dominant invariant subspace of a real matrix A by the method of simultaneous iteration. Specifically, given an integer m , SRRIT computes a matrix Q with m orthonormal columns and real quasi-triangular matrix T or order m such that the equation AQ = QT is satisfied up to a tolerance specified by the user. The eigenvalues of T are approximations to the m eigenvalues of largest absolute magnitude of A and the columns of Q span the invariant subspace corresponding to those eigenvalues. SRRIT references A only through a user-provided subroutine to form the product AQ ; hence it is suitable for large sparse problems.

In many practical direction-of-arrival (DOA) problems the number of sources and their directions from an antenna array do not remain stationary. Hence a practical DOA algorithm must be able to track changes with a minimal number of snapshots. DOA algorithms, based on a new decomposition, the URV decomposition, that are not expensive to compute or difficult to update are presented. The algorithms are compared with algorithms based on the singular value decomposition (SCD).>

An algorithm for updating the null space of a matrix is described. The algorithm is based on a decomposition, called the URV decomposition, which can be updated in O(N/sup 2/) and serves as an intermediary between the QR decomposition and the singular value decomposition. the URV decomposition is applied to a high-resolution direction-of-arrival problem based on the MUSIC algorithm. A virtue of the updating algorithm is the running estimate of rank.>

In this paper we extend a model of Karp and Miller for parallel computation. We show that the extended model is deterministic, in the sense that under different scheduling regimes each process in the computation consumes the same input and generates the same output. Moreover, if the computation halts, the final state is independent of scheduling. The model is applied to the generation of precedence graphs, from which lower time bounds may be deduced, and to the synchronization of systolic arrays by local rather than global control.

No abstract available.

An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.

A method is described for computing the steady-state probabdlty vector of a nearly completely decomposable Markov chain The method is closely related to one proposed by Simon and Ando and developed by Courtois However, the method described here does not require the determination of a completely decomposable stochastic approximation to the transition matrix, and hence it is applicable to nonstochasttc matrices An error analysis of the procedure which results in effectively computable error bounds is gwen Categories and SubJect Descriptors D.4 8 [Operating

article Free AccessArtifacts Evaluated & ReusableArtifacts Available Share on Algorithm 506: HQR3 and EXCHNG: Fortran Subroutines for Calculating and Ordering the Eigenvalues of a Real Upper Hessenberg Matrix [F2] Author: G. W. Stewart Department of Computer Science, University of Maryland, College Park, MD Department of Computer Science, University of Maryland, College Park, MDView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 2Issue 3Sept. 1976 pp 275–280https://doi.org/10.1145/355694.355700Published:01 September 1976Publication History 88citation950DownloadsMetricsTotal Citations88Total Downloads950Last 12 Months46Last 6 weeks8 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

An algorithm is proposed for calculating the eigenvectors of a diagonally dominant matrix all of whose elements are known to high relative accuracy. Eigenvectors corresponding to pathologically close eigenvalues are treated by computing the invariant subspace that they span. If the off-diagonal elements of the matrix are sufficiently small, the method is superior to standard techniques, and indeed it may produce a complete set of eigenvectors with an amount of work proportional to the square of the order of the matrix. An analysis is given of the effects of perturbations in the matrix on the eigenvectors.

A modification of Davidon's method for the unconstrained minimization of a function of several variables is proposed in which the gradient vector is approximated by differences. The step sizes for the differencing are calculated from information available in the course of the minimization and are chosen to approximately balance off the effects of truncation error and cancellation error. Numerical results and comparisons with other methods are given.