Proceedings ArticleDOI
Systolic Arrays For Eigenvalue Computation
Robert Schreiber
- Vol. 0341, pp 27-34
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TLDR
A machine architecture for computing the eigenvalues and eigenvectors of an Hermitian matrix is presented, and a one-parameter family of systems, parameterized by the bandwidth of the reduced matrix, is available.Abstract:
A machine architecture for computing the eigenvalues and eigenvectors of an Hermitian matrix is presented. Two systolic arrays are used, one for reducing full matrices to band matrices, the second for performing QR iteration on band matrices. A one-parameter family of systems, parameterized by the bandwidth of the reduced matrix, is available. This allows a tradeoff of processors for execution time.read more
Citations
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Proceedings ArticleDOI
Fault-Tolerant Systems For The Computation Of Eigenvalues And Singular Values
Chien Yi Chen,Jacob A. Abraham +1 more
TL;DR: A new methodology to incorporate fault tolerance capability into processor arrays which have been proposed for these problems by using special properities of eigenvalues and singular values to achieve the error detection without encoding the input data.
A bibliography on parallel and vector numerical algorithms
TL;DR: This is a bibliography on numerical methods that includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing.
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Some Linear-Time Algorithms for Systolic Arrays
TL;DR: It is shown how the greatest common divisor of two polynomials of degree n over a finite field can be computed in time O(n) on a linear systolic array of O( n) cells; similarly for the GCD of two n-bit binary numbers.
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Eigenvalues of a symmetric tridiagonal matrix: A divide-and-conquer approach
A S Krishnakumar,M Morf +1 more
TL;DR: A divide-and-conquer approach to the computation of the eigenvalues of a symmetric tridiagonal matrix via the evaluation of the characteristic polynomial through a set of recursions which can be implemented on a regulartree structure.
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Adaptive algorithms for estimating the complete covariance eigenstructure
TL;DR: A new method for adaptively calculating the complete set of eigenvectors and eigenvalues of a recursively updated covariance matrix estimate is presented, based on a sequence of QR matrix factorisations.
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Systolic Arrays for (VLSI).
TL;DR: A systolic system is a network of processors which rhythmically compute and pass data through the system, and almost all processors used in the networks are identical, so that a regular flow of data is kept up in the network.
Proceedings Article
A Computational Array for the QR-Method
TL;DR: A concurrent algorithm and corresponding array for computing the triangular matrix R by Householder transformations is described and particular attention is given to issues such as broadcasting and pipelining.