We describe an approach to tensor decomposition that involves extracting a set of observable matrices from the tensor and applying an approximate joint Schur decomposition on those matrices, and we establish the corresponding firstorder perturbation bounds. We develop a novel iterative Gauss-Newton algorithm for joint matrix Schur decomposition, which minimizes a nonconvex objective over the ma...

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

Mg(OH)2 nanoparticles were synthesized by a rapid microwave reaction. The effect of sodium dodecyl sulfonate (SDS as anionic surfactant) and cetyl tri-methyl ammonium bromide (CTAB as cationic surfactant) on the morphology of magnesium hydroxide nanostructures was investigated. Multi wall carbon nano tubes was organo-modified for better dispersion in cellulose acetate matrix. The influence of M...

In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...

We follow the rules: i, j, m, n, k denote natural numbers, K denotes a field, and a, λ denote elements of K. Let us consider K, λ, n. The Jordan block of λ and n yields a matrix over K and is defined by the conditions (Def. 1). (Def. 1)(i) len (the Jordan block of λ and n) = n, (ii) width (the Jordan block of λ and n) = n, and (iii) for all i, j such that 〈i, j〉 ∈ the indices of the Jordan bloc...

In this paper, we study the problem of computing an LSP-decomposition of a matrix over a field. This decomposition is an extension to arbitrary matrices of the well-known LUP-decomposition of full rowrank matrices. We present three different ways of computing an LSPdecomposition, that are both rank-sensitive and based on matrix multiplication. In each case, for an m by n input matrix of unknown...

We present a Mueller matrix decomposition based on the differential formulation of the Mueller calculus. The differential Mueller matrix is obtained from the macroscopic matrix through an eigenanalysis. It is subsequently resolved into the complete set of 16 differential matrices that correspond to the basic types of optical behavior for depolarizing anisotropic media. The method is successfull...

Let B be a block of an Iwahori–Hecke algebra or q-Schur algebra of the symmetric group. The decomposition matrix for B may be obtained from the decomposition matrix of the corresponding block B′ in infinite characteristic by post-multiplying by an adjustment matrix; since (by a deep theorem of Ariki) there is an algorithm for computing the decomposition matrix for B′, the hard part of the decom...

In this paper we propose and study an optimization problem over a matrix group orbit that we call Group Orbit Optimization (GOO). We prove that GOO can be used to induce matrix decomposition techniques such as singular value decomposition (SVD), LU decomposition, QR decomposition, Schur decomposition and Cholesky decomposition, etc. This gives rise to a unified framework for matrix decompositio...