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In this paper we construct analytic-numerical solutions for initial-boundary value systems related to the equation $u_{t} - A u_{x x} - B u = 0$ , where $B$ is an arbitrary square complex matrix and $A$ ia s matrix such that the real part of the eigenvalues of the matrix $\frac{1}{2} (A + A^{H})$ is positive. Given an admissible error $ε$ and a finite domain $G$ , and analytic-numerical solution whose error is uniformly upper bounded by $ε$ in $G$ , is constructed.

A matrix inequality

Russell C. Thompson (1976)

Commentationes Mathematicae Universitatis Carolinae

A matrix inequality for Möbius functions.

Bordellès, Olivier, Cloitre, Benoit (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

A note on Newton and Newton-like inequalities for $M$ -matrices and for Drazin inverses of $M$ -matrices.

Neumann, Michael, Xu, Jianhong (2006)

ELA. The Electronic Journal of Linear Algebra [electronic only]

A note on the complex and real operator norms of real matrices

Michel Crouzeix (1986)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A note on the trace inequality for products of Hermitian matrix power.

Yang, Zhongpeng, Feng, Xiaoxia (2002)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

A refinement of an inequality of Johnson, Loewy and London on nonnegative matrices and some applications.

Laffey, Thomas J., Meehan, Eleanor (1998)

ELA. The Electronic Journal of Linear Algebra [electronic only]

A stronger version of matrix convexity as applied to functions of Hermitian matrices.

Kagan, Abram, Smith, Paul J. (1999)

Journal of Inequalities and Applications [electronic only]

A trace inequality for functions of triangular Hilbert-Schmidt operators

John J. Buoni (1975)

Czechoslovak Mathematical Journal

A trace inequality for positive definite matrices.

Belmega, Elena-Veronica, Lasaulce, Samson, Debbah, Mérouane (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

A Trace Inequality of John von Neumann.

L. Mirsky (1975)

Monatshefte für Mathematik

A treatment of a determinant inequality of Fiedler and Markham

Minghua Lin (2016)

Czechoslovak Mathematical Journal

Fiedler and Markham (1994) proved ${(\frac{\det \hat{H}}{k})}^{k} \geq \det H,$ where $H = {(H_{i j})}_{i, j = 1}^{n}$ is a positive semidefinite matrix partitioned into $n \times n$ blocks with each block $k \times k$ and $\hat{H} = {(tr H_{i j})}_{i, j = 1}^{n}$ . We revisit this inequality mainly using some terminology from quantum information theory. Analogous results are included. For example, under the same condition, we prove $\det (I_{n} + \hat{H}) \geq \det {(I_{n k} + k H)}^{1 / k} .$

Actions of the symmetric group generated by comparable sets of integers and Smith invariants.

Azenhas, Olga, Mamede, Ricardo (2007)

Séminaire Lotharingien de Combinatoire [electronic only]

Admissible estimators in the general multivariate linear model with respect to inequality restricted parameter set.

Zhang, Shangli, Liu, Gang, Gui, Wenhao (2009)

Journal of Inequalities and Applications [electronic only]

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