On Hermitian positive definite solution of the matrix equation X−∑i=1mAi∗XrAi=Q [PDF]
, 2009 A conjecture that the nonlinear matrix equation X−∑i=1mAi∗XrAi=Q(−1 ...
Duan, Xuefeng, Liao, Anping
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Continuation of Radial Positive Definite Functions and Their Characterization
Fractal and Fractional, 2023 This paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann–Liouville fractional integral and fractional Caputo derivatives ...
Fethi Bouzeffour
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Bounded real lemmas for positive descriptor systems [PDF]
, 2015 A well known result in the theory of linear positive systems is the existence of positive definite diagonal matrix (PDDM) solutions to some well known linear matrix inequalities (LMIs).
Yan, Xinggang +3 more
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The rank-constrained Hermitian nonnegative-definite and positive-definite solutions to the matrix equation AXA∗=B [PDF]
, 2003 A simple representation of the general rank-constrained Hermitian nonnegative-definite (positive-definite) solution to the matrix equation AXA∗=B is derived.
Zhang, Xian, Cheng, Mei-yu
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A Fixed Point Theorem for Monotone Maps and Its Applications to Nonlinear Matrix Equations
Journal of Mathematics, 2015 By using the fixed point theorem for monotone maps in a normal cone, we prove a uniqueness theorem for the positive definite solution of the matrix equation X=Q+A⁎f(X)A, where f is a monotone map on the set of positive definite matrices.
Dongjie Gao
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Approximation of a Solution for aK-Positive Definite Operator Equation [PDF]
, 1997 LetEbe separableq-uniformly smooth Banach space,q>1, and letA:D(A)⊆E→Ebe aK-positive definite operator. Letf∈Ebe arbitrary. An iterative method is constructed which converges strongly to the unique solution of the equationAx=f.
Chidume, C.E., Osilike, M.O.
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Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I
Abstract and Applied Analysis, 2015 We investigate the nonlinear matrix equation Xr-∑i=1mAi∗X-δiAi=I, where r is a positive integer and δi∈(0,1], for i=1,2,…,m. We establish necessary and sufficient conditions for the existence of positive definite solutions of this equation.
Asmaa M. Al-Dubiban
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Conditionally positive definite kernels on Euclidean domains [PDF]
, 2004 This paper characterizes several classes of conditionally positive definite kernels on a domain Ω of either Rl or Cl. Among the classes is that composed of strictly conditionally positive definite kernels.
Menegatto, V.A., Peron, A.P.
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Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X-1A=L
Open Mathematics, 2015 In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for
Adam Maria, Assimakis Nicholas
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The positive definite completion problem revisited [PDF]
, 2008 In [R. Grone, C.R. Johnson, E. Sa, H. Wolkowicz, Positive definite completions of partial Hermitian matrices, Linear Algebra Appl. 58 (1984) 109–124] the positive definite (semi-) completion problem in which the underlying graph is chordal was solved ...
Smith, Ronald L.
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