Condition numbers of large matrices, and analytic capacities

DOI10.1090/S1061-0022-06-00924-1zbMath1098.15002OpenAlexW1597018060MaRDI QIDQ5477787

Nikolai Nikolski

Publication date: 29 June 2006

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-06-00924-1

zbMATH Keywords

capacityBesov spacescondition numbersspectral condition numberWiener algebrafunctional calculusalgebraic operatorsfunction algebrasBanach space Kreiss operatorsBanach space Tadmor-Ritt operatorsHilbert space power bounded operators

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Functional calculus for linear operators (47A60) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12) Algebras of holomorphic functions of several complex variables (32A38)

Related Items (18)

On the asymptotic behavior of Jacobi polynomials with first varying parameter ⋮ Sharp estimate on the resolvent of a finite-dimensional contraction ⋮ Maximum of the resolvent over matrices with given spectrum ⋮ \(l_p\)-norms of Fourier coefficients of powers of a Blaschke factor ⋮ On the condition number of a Kreiss matrix ⋮ \(H^{\infty}\) interpolation and embedding theorems for rational functions ⋮ Stationary phase method, powers of functions, and applications to functional analysis ⋮ Explicit counterexamples to Schäffer's conjecture ⋮ Spectral variation bounds in hyperbolic geometry ⋮ Perturbation bounds for quantum Markov processes and their fixed points ⋮ Norm controlled inversions and a corona theorem for \(H^\infty \)-quotient algebras ⋮ Condition numbers of matrices with given spectrum ⋮ On Bernstein's inequality for polynomials ⋮ Sharpening a result by E. B. Davies and B. Simon ⋮ Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle ⋮ Spectral convergence bounds for classical and quantum Markov processes ⋮ Interpolation with constraints on the finite sets of the disc ⋮ Toeplitz condition numbers as an \(H^{\infty }\) interpolation problem

Cites Work

• Zeros of analytic functions and norms of inverse matrices
• Spectral theory of approximation methods for convolution equations
• In search of the invisible spectrum
• Extremal growth of powers of operators satisfying resolvent conditions of Kreiss-Ritt type
• Functional calculus under the Tadmor--Ritt condition, and free interpolation by polynomials of a given degree
• Norms and determinants of linear mappings
• Some remarks on Q-algebras
• Sets of uniqueness for functions regular in the unit circle
• Functional calculus under Kreiss type conditions
• On the Eigenvalues of a Matrix with Prescribed Singular Values
• Inequalities: theory of majorization and its applications
• Potential theory
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