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Some investigation on Hermitian positive definite solutions of the matrix equation Xs+A∗X-tA=Q [PDF]
Linear Algebra and Its Applications, 2009 In this paper, the Hermitian positive definite solutions of the matrix equation Xs+A∗X-tA=Q are considered, where Q is an Hermitian positive definite matrix, s and t are positive integers.
Cai, Jing, Chen, Guoliang
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Complex Analysis and Operator Theory, 2014
The authors study how orthogonal matrix polynomials and related second kind polynomials which correspond to sequences generated by right(left)-sided \(\alpha\)-shifting [\textit{B. Fritzsche} et al., Linear Algebra Appl. 439, No. 12, 3893--3933 (2013; Zbl 1283.44003)] or by ``two-sided'' \(a-b\)-shifting are connected with polynomials generated by the ...
Rivero, Abdon E. Choque, Mädler, Conrad
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The authors study how orthogonal matrix polynomials and related second kind polynomials which correspond to sequences generated by right(left)-sided \(\alpha\)-shifting [\textit{B. Fritzsche} et al., Linear Algebra Appl. 439, No. 12, 3893--3933 (2013; Zbl 1283.44003)] or by ``two-sided'' \(a-b\)-shifting are connected with polynomials generated by the ...
Rivero, Abdon E. Choque, Mädler, Conrad
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Integral representation of invariant positive-definite matrix kernels
Ukrainian Mathematical Journal, 1970zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Samoĭlenko, Yu. S., Korsunskiĭ, L. M.
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The Eigenvalues of Complementary Principal Submatrices of a Positive Definite Matrix
Canadian Journal of Mathematics, 1972Let C be an n-square Hermitian matrix, presented in partitioned form aswhere A is a-square and B is b-square. Let denote the eigenvalues of C, A, B, respectively. In a recent paper [10] the following inequality was established:1.1if1.2This inequality is a ...
Thompson, R. C., Therianos, S.
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Positive definite matrix approximation with condition number constraint
Optimization Letters, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mirai TANAKA, Kazuhide Nakata
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A positive-definite matrix which is not extendible
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1984This note treats the problem of extendibility of a positive-definite matrix. The difference between extendibility and positive- semidefiniteness in multiple dimensions is described. The construction of a positive definite nonextendible correlation matrix is also given.
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Computing the Smallest Eigenpair of a Symmetric Positive Definite Toeplitz Matrix
SIAM Journal on Scientific Computing, 1999The smallest eigenvalue of a symmetric positive definite Toeplitz matrix is computed by a Newton algorithm, using a Levinson-Durbin recursion to evaluate the characteristic polynomial. Eigenvectors are delivered, error bounds and numerical tests are reported.
Nicola Mastronardi, Daniel Boley
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Positive-Definite Matrix Processes of Finite Variation
2006Processes of finite variation, which take values in the positive semidefinite matrices and are representable as the sum of an integral with respect to time and one with respect to an extended Poisson random measure, are considered. For such processes we derive conditions for the square root (and the r-th power with 0 < r < 1) to be of finite ...
Barndorff-Nielsen, Ole Eiler +1 more
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Symmetric decomposition of a positive definite matrix
Numerische Mathematik, 1965Martin, R. S. +2 more
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On Orthogonal Polynomials With Respect to a Positive Definite Matrix of Measures
Canadian Journal of Mathematics, 1995AbstractIn this paper, we prove that any sequence of polynomials (pn)n for which dgr(pn) = n which satisfies a (2N + l)-term recurrence relation is orthogonal with respect to a positive definite N × N matrix of measures. We use that result to prove asymptotic properties of the kernel polynomials associated to a positive measure or a positive definite ...
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