Minimum \(w\)-entropy interpolants for matricial Carathéodory functions and maximum determinant completions of associated block Pick matrix

DOI10.1016/j.laa.2010.11.051zbMath1222.47018OpenAlexW2024096078MaRDI QIDQ630537

Gong-Ning Chen, Yong-jian Hu

Publication date: 17 March 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.11.051

zbMATH Keywords

Nevanlinna-Pick type interpolation\(w\)-entropy integralCarathéodory coefficient problemmatricial Carathéodory functionmaximum determinant completions

Mathematics Subject Classification ID

Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear operator methods in interpolation, moment and extension problems (47A57) Moment problems and interpolation problems in the complex plane (30E05)

Cites Work

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• On the largest minorants associated with a matrix-valued Carathéodory function and spectral factorization
• On rank invariance of generalized Schwarz--Pick--Potapov block matrices of matrix-valued Carathéodory functions
• On hermitian block Hankel matrices, matrix polynomials, the Hamburger moment problem, interpolation and maximum entropy
• On the multiple Nevanlinna-Pick matrix interpolation in the class \(\mathcal C_p\) and the Carathéodory matrix coefficient problem
• Problem of search of the minimum of entropy in indeterminate extension problems
• Interpolation of rational matrix functions
• On degenerate interpolation, entropy and extremal problems for matrix Schur functions
• On maximum entropy interpolants and maximum determinant completions of associated Pick matrices
• More on maximum entropy interpolants and maximum determinant completions of associated Pick matrices
• An Extension Problem for Non-Negative Hermitian Block Toeplitz Matrices
• The Nevanlinna–Pick Problem for Matrix-Valued Functions
• An inverse entropy optimization problem for matrix-valued carathéodory functions
• On a class of extremal solutions of the nondegenerate matricial Carathéodory problem
• Solution of a multiple Nevanlinna–Pick problem for Carathéodory functions via orthogonal rational functions in the matrix case

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