On matrix coefficients of the Satake isomorphism: complements to the paper of M. Rapoport

2000 ◽  
Vol 101 (2) ◽  
pp. 167-174 ◽  
Author(s):  
Thomas J. Haines
Keyword(s):  
Matrix Coefficients ◽  
Satake Isomorphism

scholarly journals Approximated least-squares solutions of a generalized Sylvester-transpose matrix equation via gradient-descent iterative algorithm

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam
Keyword(s):  
Least Squares ◽  
Iterative Algorithm ◽  
Gradient Descent ◽  
Main Idea ◽  
Full Column Rank ◽  
Minimum Error ◽  
Matrix Coefficients ◽  
Special Cases ◽  
Efficiency And Effectiveness ◽  
Associated Matrix

AbstractThis paper proposes an effective gradient-descent iterative algorithm for solving a generalized Sylvester-transpose equation with rectangular matrix coefficients. The algorithm is applicable for the equation and its interesting special cases when the associated matrix has full column-rank. The main idea of the algorithm is to have a minimum error at each iteration. The algorithm produces a sequence of approximated solutions converging to either the unique solution, or the unique least-squares solution when the problem has no solution. The convergence analysis points out that the algorithm converges fast for a small condition number of the associated matrix. Numerical examples demonstrate the efficiency and effectiveness of the algorithm compared to renowned and recent iterative methods.

General finite-volume framework for saddle-point problems of various physics

2021 ◽  
Vol 36 (6) ◽  
pp. 359-379
Author(s):  
Kirill M. Terekhov
Keyword(s):  
Saddle Point ◽  
Finite Volume ◽  
Navier Stokes ◽  
Saddle Point Problems ◽  
Surface Integral ◽  
Matrix Coefficients ◽  
Gauss Theorem ◽  
Stability Issue ◽  
Incompressible Elasticity ◽  
Vector Flux

Abstract This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.

A ray expansion with matrix coefficients for sourcesin absorbing anisotropic media

1976 ◽  
Vol 15 (1) ◽  
pp. 151-163 ◽  
Author(s):  
J. A. Bennett
Keyword(s):  
Mode Coupling ◽  
Homogeneous Medium ◽  
Anisotropic Media ◽  
Far Field ◽  
Wave Polarization ◽  
Problem Method ◽  
Matrix Coefficients ◽  
Leading Term ◽  
Green’S Matrix ◽  
Complex Rays

A ray or quasi-optical approximation is developed, using complex rays. The ‘amplitude’ terms are matrices, rather than vectors that represent the wave polarization. Thus, the way the propagation resolves a source into various modes is described. The second term in the amplitude series is shown to include a type of inter-mode coupling. It is shown that initial values needed to integrate along the rays can be chosen so that the leading term of the approximation agrees with the far-field solution for localized sources in a homogeneous medium. By invoking the ‘canonical problem’ method, the result is extended to give an approximation for the Green's matrix in a slowly-varying medium.

scholarly journals Quality yarn index using AHP and Fuzzy method

2020 ◽  
Vol 71 (05) ◽  
pp. 487-491
Author(s):  
MOHAMED BEN HASSEN ◽  
MOHAMED TAHER HALIM ◽  
EMAD ABUALSAUOD ◽  
ASEM OTHMAN
Keyword(s):  
Fuzzy Theory ◽  
Relative Importance ◽  
Analytic Hierarchy ◽  
Yarn Quality ◽  
Multicriteria Problem ◽  
Global Quality ◽  
Matrix Coefficients ◽  
Mechanical And Physical Properties ◽  
Hierarchy Process

The yarn quality depends on many parameters: characteristics parameters, mechanical and physical properties. Making the hypothesis that the quality of the yarn is a multicriteria problem, in this paper, we propose a new method to determine the Quality Yarn Index QYI based on Analytic Hierarchy Process AHP and Fuzzy theory. A questionnaire was designed for experts of each field (weaving and knitting) to evaluate the relative importance for each property to determine coefficients of the AHP matrix. Results revealed that matrix coefficients changed with yarn application (weft or warp weaving and knitting) The QYI can be used in any application, where a rapid decision is needed, to evaluate the global quality of yarn and to make a comparison between different yarn qualities

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