Matrix-vector Multiplication Algorithm Research Articles

Optical complex matrix–vector multiplication with negative binary inner products

Based on the mixed negative binary number system, we propose an inner-product algorithm for digital complex-valued matrix-vector multiplication. The features are no carries, no signs, no indications for decimal points, and simple preprocessing and postprocessing. Correspondingly, an optical architecture of incoherent optical correlation with spatial digital coding of data is suggested. Negative binary complex matrix-vector multiplication can be realized optically in parallel with a high accuracy. The experimental result is also given.

Fast Multiresolution Algorithms for Matrix-Vector Multiplication

In this paper the authors present a class of multiresolution algorithms for fast application of structured dense matrices to arbitrary vectors, which includes the fast wavelet transform of Beylkin, Coifman, and Rokhlin and the multilevel matrix multiplication of Brandt and Lubrecht. In designing these algorithms the authors first apply data compression techniques to the matrix and then show how to compute the desired matrix-vector multiplication from the compressed form of the matrix. In describing this class special attention is paid to an algorithm that is based on discretization by cell-averages as it seems to be suitable for discretization of integral transforms with integrably singular kernels.

Sparse matrix vector multiplication techniques on the IBM 3090 VF

This article demonstrates the benefits of applying Fortran programming techniques based on outer loop vectorization and the multiply-and-add compound instruction to the implementation of several sparse matrix vector multiplication algorithms on the IBM 3090 VF. The discussed algorithms use the scalar and vector ITPACK storage schemes and some variants of them. Their performance is analysed by comparing the execution rates and the storage requirements for several test matrices from the Harwell-Boeing collection.

Implementing linear algebra algorithms on a Meiko computing surface

This paper reports some performance tests on a parallel computing system with distributive memory. A number of tests concerns speed of communication. Others concern performance of floating-point calculations; most of these tests concern the speed of a single processor. Two experiments are reported on the implementation of methods for solving a bidiagonal and a tridiagonal linear system respectively. The algorithms are of the divide-and-conquer type. An algorithm for matrix-vector multiplication on a square grid of processors is also reported.

Optical implementation of systolic array processing

We show how certain algorithms for matrix-vector multiplication can be implemented using acoustooptic cells for multiplication and input data transfer and using CCD detector arrays for accumulation and output of the results. No 2-D matrix mask is required; matrix changes are implemented electronically. A system for multiplying a 50-component nonnegative- real matrix is described. Modifications for bipolar-real and complex-valued processing are possible, as are extensions to matrix—matrix multiplication and multiplication of a vector by multiple matrices.