‎The global generalized minimum residual (Gl-GMRES)‎ ‎method is examined for solving the generalized Sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {A_i } XB_i = C.]‎ ‎Some new theoretical results are elaborated for‎ ‎the proposed method by employing the Schur complement‎. ‎These results can be exploited to establish new convergence properties‎ ‎of the Gl-GMRES method for solving genera...

We present a method of obtaining WKB type solutions for generalized .~ Schroedinger equations for which the Hamiltonian is an arbitrary matrix function of any.number of pairs of canonical operators. Our solution reduces the problem to that of finding the matrix which diagonalizes the classical Hamiltonian and determining the scalar WKB wave functions for the diagonalized Hamiltonian's entries (...

Matrix factorization algorithms are emerging as popular tools in many applications, especially dictionary learning method for recovering biomedical image data from noisy and ill-conditioned measurements. We introduce a novel dictionary learning algorithm based on augmented Lagrangian (AL) approach to learn dictionaries from exemplar data and it can be extended to general matrix factorization pr...

A general form of the polarization matrix valid for any type of electromagnetic radiation (plane waves, multipole radiation etc.) is defined in terms of a certain bilinear form in the field-strength tensor. The quantum counterpart is determined as an operator matrix with normal-ordered elements with respect to the creation and annihilation operators. The zero-point oscillations (ZPO) of polariz...

Amino acid replacement matrices are an essential basis of protein phylogenetics. They are used to compute substitution probabilities along phylogeny branches and thus the likelihood of the data. They are also essential in protein alignment. A number of replacement matrices and methods to estimate these matrices from protein alignments have been proposed since the seminal work of Dayhoff et al. ...

We present a formulation of a matrix model which manifestly possesses the general coordinate invariance when we identify the large N matrices with differential operators. In order to build a matrix model which has the local Lorentz invariance, we investigate how the so(9, 1) Lorentz symmetry and the u(N) gauge symmetry are mixed together. We first analyze the bosonic part of the model, and we f...

1. An O(mm(n) log(n)) = O(nω+ ) algorithm which finds the shortest distance matrix for a graph G by recursively finding the shortest distance matrix for the graph G2. 2. The problem of determining the successor matrix for tripartite graphs. 3. O(nω) time algorithm for finding successor matrix in in a simple tripartite graph when there is a unique successor for any 2 vertices. 4. An O(mm(n) log(...

We develop a unified and systematic framework for performing online nonnegative matrix factorization under a wide variety of important divergences. The online nature of our algorithm makes it particularly amenable to large-scale data. We prove that the sequence of learned dictionaries converges almost surely to the set of critical points of the expected loss function. We do so by leveraging the...

Matrix factorization is among the most successful techniques for collaborative filtering. One challenge of collaborative filtering is how to utilize available auxiliary information to improve prediction accuracy. In this paper, we study the problem of utilizing auxiliary information as features of factorization and propose formalizing the problem as general functional matrix factorization, whos...

In this article the general non-symmetric parametric form of the incremental secant stiffness matrix for nonlinear analysis of solids have been investigated to present a semi analytical sensitivity analysis approach for geometric nonlinear shape optimization. To approach this aim the analytical formulas of secant stiffness matrix are presented. The models were validated and used to perform inve...