Domain decomposition (DD) methods are widely used as preconditioner techniques. Their effectiveness relies on the choice of a locally constructed coarse space. Thus far, this construction was mostly achieved using nonassembled matrices from discretized partial differential equations (PDEs). Therefore, DD were mainly successful when solving systems stemming PDEs. In paper, we present fully algeb...

A quadratically convergent Newton method for computing the polar decomposition of a full-rank matrix is presented and analysed. Acceleration parameters are introduced so as to enhance the initial rate of convergence and it is shown how reliable estimates of the optimal parameters may be computed in practice. To add to the known best approximation property of the unitary polar factor, the Hermit...

The number of multiplications required for matrix multiplication, for the triangular decomposition of a matrix with partial pivoting, and for the Cholesky decomposition of a positive definite symmetric matrix, can be roughly halved if Winograd’s identity is used to compute the inner products involved. Floating-point error bounds for these algorithms are shown to be comparable to those for the n...

Given a symmetric and positive (semi)definite n-by-n matrix M and a vector, in this paper, we consider the matrix splitting method for solving the second-order cone linear complementarity problem (SOCLCP). The matrix splitting method is among the most widely used approaches for large scale and sparse classical linear complementarity problems (LCP), and its linear convergence is proved by [Luo a...

in this paper, some elementary operations on triangular fuzzynumbers (tfns) are defined. we also define some operations on triangularfuzzy matrices (tfms) such as trace and triangular fuzzy determinant(tfd). using elementary operations, some important properties of tfms arepresented. the concept of adjoints on tfm is discussed and some of theirproperties are. some special types of tfms (e.g. pu...

This paper studies off-diagonal decay in symmetric Toeplitz matrices. It is shown that if the generating sequence of the matrix is monotone, positive and convex then the monotonicity and positivity are maintained through triangular decomposition. The work is motivated by recent results on explicit bounds for inverses of triangular matrices. © 2005 Elsevier Inc. All rights reserved. AMS classifi...

Least squares approximation of a symmetric matrix C by a symmetric positive definite matrix Ĉ of rank at most p is a classical problem. It is typically solved by computing an eigen-decomposition of C and by truncating the eigen-decomposition by only using the eigenvectors and associated with the min(p, q) largest positive eigenvalues of C. Here q is the number of positive eigenvalues. Thus if q...