Results 21 to 30 of about 95 (94)

Direct methods for matrix Sylvester and Lyapunov equations

Journal of Applied Mathematics, Volume 2003, Issue 6, Page 277-303, 2003., 2003
We revisit the two standard dense methods for matrix Sylvester and Lyapunov equations: the Bartels‐Stewart method for A1X + XA2 + D = 0 and Hammarling′s method for AX + XAT + BBT = 0 with A stable. We construct three schemes for solving the unitarily reduced quasitriangular systems. We also construct a new rank‐1 updating scheme in Hammarling′s method.
Danny C. Sorensen, Yunkai Zhou
wiley   +1 more source

The core inverse and constrained matrix approximation problem

Open Mathematics, 2020
In this article, we study the constrained matrix approximation problem in the Frobenius norm by using the core inverse:||Mx−b||F=minsubjecttox∈ℛ(M),||Mx-b|{|}_{F}=\hspace{.25em}\min \hspace{1em}\text{subject}\hspace{.25em}\text{to}\hspace{1em}x\in ...
Wang Hongxing, Zhang Xiaoyan
doaj   +1 more source

The Cayley transform of Banach algebras

International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 7, Page 427-428, 2002., 2002
The main result of Haynes (1991) is that a square matrix is convergent (limn→∞Dn = 0) if and only if it is the Cayley transform CA = (I−A)−1(I + A) of a stable matrix A. In this note, we show, with a simple proof, that the above is true in a much more general setting of complex Banach algebras.
Zhidong Pan
wiley   +1 more source

A projector oriented approach to the best linear unbiased estimator [PDF]

General Gauss–Markov model, Ordinary least squares estimator, Oblique projector, Generalized projection operator, 62J05, 62H12, 15A24, 15A57,
Oskar Baksalary, Götz Trenkler
core   +1 more source

Invariance of recurrence sequences under a galois group

International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 327-334, 1996., 1995
Let F be a Galois field of order q, k a fixed positive integer and R = Fk×k[D] where D is an indeterminate. Let L be a field extension of F of degree k. We identify Lf with fk×1 via a fixed normal basis B of L over F. The F‐vector space Γk(F)( = Γ(L)) of all sequences over Fk×1 is a left R‐module. For any regular f(D) ∈ R, Ωk(f(D)) = {S ∈ Γk(F) : f(D)S
Hassan Al-Zaid, Surjeet Singh
wiley   +1 more source

Generalized Pell Equations for 2 × 2 Matrices

Discussiones Mathematicae - General Algebra and Applications, 2017
In this paper we consider the solutions of the generalized matrix Pell equations X2 − dY2 = cI, where X and Y are 2 × 2 matrices over ℤ, d is a non-zero (positive or negative) square-free integer, c is an arbitrary integer and I is the 2 × 2 identity ...
Cohen Boaz
doaj   +1 more source

Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 1, Page 91-102, 1994., 1994
In this paper, we develop a Frobenius matrix method for solving higher order systems of differential equations of the Fuchs type. Generalized power series solution of the problem are constructed without increasing the problem dimension. Solving appropriate algebraic matrix equations a closed form expression for the matrix coefficient of the series are ...
E. Navarro, L. Jódar, R. Company
wiley   +1 more source

Generalized Green′s functions for higher order boundary value matrix differential systems

International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 3, Page 523-535, 1992., 1992
In this paper, a Green′s matrix function for higher order two point boundary value differential matrix problems is constructed. By using the concept of rectangular co‐solution of certain algebraic matrix equation associated to the problem, an existence condition as well as an explicit closed form expression for the solution of possibly not well‐posed ...
R. J. Villanueva, L. Jodar
wiley   +1 more source

A Comprehensive Review of Matrix Equations in Dynamical Systems and Control Theory

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
Matrix equations are of foundational importance in the modeling, investigation, and control of dynamical systems. This review discusses various classes of matrix equations, their solutions, and their relevance in control theory and dynamical systems.
Chacha Stephen Chacha, Arpan Hazra
wiley   +1 more source

Stable matrices, the Cayley transform, and convergent matrices

International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 1, Page 77-81, 1991., 1991
The main result is that a square matrix D is convergent () if and only if it is the Cayley transform CA = (I − A) −1(I + A) of a stable matrix A, where a stable matrix is one whose characteristic values all have negative real parts. In passing, the concept of Cayley transform is generalized, and the generalized version is shown closely related to the ...
Tyler Haynes
wiley   +1 more source