# Delosme, J.-M

Overview
Works: 9 works in 11 publications in 1 language and 15 library holdings Author QA188,
Publication Timeline
.
Most widely held works by J.-M Delosme
The Cholesky factorization, Schur complements, correlation coefficients, angles between vectors, and the QR factorization by J.-M Delosme( Book )

3 editions published in 1988 in English and held by 7 WorldCat member libraries worldwide

An m x m symmetric nonnegative definite matrix Sigma has Cholesky factorization Sigma = u-transpose u. By carrying out the factorization in a particular way for positive definite Sigma, the Schur complements of all the leading principal submatrices of Sigma are produced, as well as their Cholesky factors. It is shown how the same can be done for generalized Schur complements when Sigma is singular. When Sigma is the population covariance matrix of a multivariate random distribution, partial covariances and correlations can be defined in terms of the elements of such Schur complements. It follows that these can be produced efficiently and reliably from the Cholesky factorization. When n x m A is given and Sigma = A-transpose A, the Cholesky factor U may be found directly from the QR factorization A = Q1U, Q1-transpose Q1 = I, and this is preferable in many numerical computations. This QR factorization, or the modified Gram-Schmidt orthogonalization, produces projections of later columns of A onto spaces orthogonal to earlier columns. It is shown how the cosines of the angles between such projected vectors can be found using the elements of U. These cosines produced from A turn out to be the previously mentioned partial correlation coefficients produced from Sigma, when Sigma = A-transpose A. When A is obtained from observations of random variables, these are the sample correlation coefficients. It is shown how such correlation coefficients can be efficiently obtained when observations are added or deleted. This corresponds to altering all of A in a certain simple way, and adding or deleting rows
Optimization of computation time for systolic arrays by Joyce Y Wong( )

1 edition published in 1992 in English and held by 1 WorldCat member library worldwide

Parallel solution of symmetric positive definite systems with hyperbolic rotations by J.-M Delosme( Book )

1 edition published in 1985 in English and held by 1 WorldCat member library worldwide

Transformation of broadcasts into propagations in systolic algorithms by Yale University( Book )

1 edition published in 1989 in English and held by 1 WorldCat member library worldwide

Optimization of processor count for systolic arrays by Yale University( Book )

1 edition published in 1989 in English and held by 1 WorldCat member library worldwide

Parallel singular value decompotision of complex matrices using multidimensional CORDIC algorithms by S. F Hsiao( )

1 edition published in 1996 in English and held by 1 WorldCat member library worldwide

Optimization of computation time for systolic arrays by Yale University( Book )

1 edition published in 1989 in English and held by 1 WorldCat member library worldwide

Efficient Parallel Solution of Linear Systems with Hyperbolic Rotations by Jean-Marc Delosme( Book )

1 edition published in 1984 in English and held by 1 WorldCat member library worldwide

An algorithm based on hyperbolic rotations is presented for the solution of linear systems of equations, Ax = b, with symmetric positive definite coefficient matrix A. Forward elimination and backsubstitution are replaced by matrix vector multiplications, rendering the method most amenable to implementation on a variety of parallel and vector machines. The stability behaviour compares favourably with that of the best, known methods. The method can be simplified and formulated without square roots if A is also Toeplitz; a corresponding systolic architecture (in very large scale integrated circuits) for the resulting recurrence equations is more efficient than previously proposed pipelined Toeplitz system solvers. The hardware count becomes independent of the matrix size if its inverse is banded
Space and time bases for the sequentialization of systolic array designs by Yale University( Book )

1 edition published in 1991 in English and held by 1 WorldCat member library worldwide

Audience Level
 0 1 Kids General Special

Related Identities
Languages
English (11)