Computing the Combinatorial Canonical Form of a Layered Mixed Matrix
نویسندگان
چکیده
This paper presents an improved algorithm for computing the Combinatorial Canonical Form (CCF) of a layered mixed matrix A = Q T , which consists of a numerical matrix Q and a generic matrix T . The CCF is the (combinatorially unique) nest block-triangular form obtained by the row operations on the Q-part, followed by permutations of rows and columns of the whole matrix. The main ingredient of the improvements is the introduction of two precalculation phases. Computational results are also reported.
منابع مشابه
Determination of a Matrix Function in the Form of f(A)=g(q(A)) Where g(x) Is a Transcendental Function and q(x) Is a Polynomial Function of Large Degree Using the Minimal Polynomial
Matrix functions are used in many areas of linear algebra and arise in numerical applications in science and engineering. In this paper, we introduce an effective approach for determining matrix function f(A)=g(q(A)) of a square matrix A, where q is a polynomial function from a degree of m and also function g can be a transcendental function. Computing a matrix function f(A) will be time- consu...
متن کاملOn the Kronecker Canonical Form of Singular Mixed Matrix Pencils
Dynamical systems, such as electric circuits, mechanical systems, and chemical plants, can be modeled by mixed matrix pencils, i.e., matrix pencils having two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. Based on dimension analysis of dynamical systems, Murota (1985) introduced a physically ...
متن کاملMixed Matrices — Irreducibility and Decomposition — ∗
This paper surveys mathematical properties of (layered-) mixed matrices with emphasis on irreducibility and block-triangular decomposition. A matrix A is a mixed matrix if A = Q + T , where Q is a “constant” matrix and T is a “generic” matrix (or formal incidence matrix) in the sense that the nonzero entries of T are algebraically independent parameters. A layered mixed (or LM-) matrix is a mix...
متن کاملThermal Behavior of a New Type of Multi-Layered Porous Air Heater
Based on an effective energy conversion method between gas enthalpy and thermal radiation, a multi-layered type of porous air heater has been proposed. In the five layered structure which is analyzed in this work, there are five porous layers which are separated by four quartz glass windows. The main layer operates as a porous radiant burner that products a large amount of thermal radiative ene...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS On Kronecker Canonical Form of Mixed Matrix Pencils
A mixed matrix pencil is a matrix pencil which has two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. In this paper, we characterize the indices of nilpotency of the Kronecker canonical form for a mixed matrix pencil in terms of matroids. As a byproduct, we provide an algorithm for computing t...
متن کامل