Numerical algorithms for the Nevanlinna-Pick problem

DOI10.1007/BF01395306zbMath0529.65006MaRDI QIDQ787641

A. C. Allison, N. J. Young

Publication date: 1983

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132866

zbMATH Keywords

numerical resultsNevanlinna-Pick interpolation problemHankel operatorbounded analytic functionspolesminimal norm solutionsingular value probleminfinite Hankel matrix

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Linear operators on function spaces (general) (47B38)

Related Items

Computing matrix-valued Nevanlinna-Pick interpolation ⋮ Tracking poles, representing Hankel operators, and the Nehari problem ⋮ Balanced minimal realization via singular value decomposition of Sarason operator ⋮ The scalar Nevanlinna-Pick interpolation problem with boundary conditions ⋮ Multi-point degenerate interpolation problem for generalized Schur functions: description of all solutions ⋮ Nevanlinna-Pick interpolation by rational functions with a single pole inside the unit disk ⋮ Factorization and the Schur-Cohn matrix of a matrix polynomial ⋮ Sarason approach to optimal, 2-block and 4-block \(H^ \infty\) norm ⋮ A new algorithm for meromorphic Nevanlinna-Pick interpolation ⋮ Parallel algorithms for nevanlinna-pick interpolation:the scalar case^∗ ⋮ Applications of Pick-Nevanlinna interpolation theory to retention- solubility studies in the lungs ⋮ Hankel matrices and minifunctions

Cites Work

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• Functions of operators and the spectral radius
• The distance of a function to \(H^\infty\) in the Poincaré metric; electrical power transfer
• The singular-value decomposition of an infinite Hankel matrix
• On the role of the Nevanlinna–Pick problem in circuit and system theory
• The solution of Lyapunov's matrix equation by a geometric method
• Generalized Interpolation in H ∞
• ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM