A generalization of the numerical range of a matrix

DOI10.1016/0024-3795(90)90232-2zbMath0712.15027OpenAlexW2044462063MaRDI QIDQ923679

H. W. J. Lenferink, Marc N. Spijker

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0024-3795(90)90232-2

zbMATH Keywords

numerical rangematrix normgeneralized numerical rangeHermitian adjointresolvent inequality

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (18)

On the geometry of the envelope of a matrix ⋮ Stability estimates based on numerical ranges with an application to a spectral method ⋮ Error growth analysis via stability regions for discretizations of initial value problems ⋮ Stability estimates for families of matrices of nonuniformly bounded order ⋮ On the numerical radius of matrices and its application to iterative solution methods ⋮ Birkhoff-James approximate orthogonality sets and numerical ranges ⋮ An algorithm to compute sets enclosingM-numerical ranges with applications in numerical analysis ⋮ Maximum norm contractivity of discretization schemes for the heat equation ⋮ Fields of values and iterative methods ⋮ \(a\)-numerical range on \(C^{\ast}\)-algebras ⋮ Resolvent conditions for discretizations of diffusion-convection-reaction equations in several space dimensions ⋮ Resolvent conditions and bounds on the powers of matrices, with relevance to numerical stability of initial value problems ⋮ Numerical ranges and stability estimates ⋮ A note about ritt's condition, related resolvent conditions and power bounded operators ⋮ On the continuity of Birkhoff–James -orthogonality sets ⋮ Stability of the method of lines ⋮ Stability in the numerical solution of the heat equation with nonlocal boundary conditions ⋮ Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semigroups of linear operators and applications to partial differential equations
• Bounds on nonlinear operators in finite-dimensional Banach spaces
• On multistep approximation of semigroups in Banach spaces
• Relatively bounded matrix sets, minimal matrix norms and numerical ranges
• Elementary inclusion relations for generalized numerical ranges
• Norm properties of C-numerical radii
• The Bauer fields of values of a matrix
• On convexity properties of the Bauer field of values of a matrix
• Stability of difference schemes in the maximum-norm
• On the field of values subordinate to a norm
• On the Use of Stability Regions in the Numerical Analysis of Initial Value Problems
• Matrix Analysis
• On Rational Approximations of Semigroups

This page was built for publication: A generalization of the numerical range of a matrix