A Krylov Subspace Method for the Approximation of Bivariate Matrix Functions

DOI10.1007/978-3-030-04088-8_10zbMath1451.65050arXiv1802.05759OpenAlexW2787172707MaRDI QIDQ3294692

Daniel Kressner

Publication date: 29 June 2020

Published in: Structured Matrices in Numerical Linear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.05759

zbMATH Keywords

Fréchet derivativeKrylov subspace methodSylvester equationmatrix functionbivariate polynomial

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Multilinear algebra, tensor calculus (15A69) Numerical methods for matrix equations (65F45)

Related Items (9)

Mixed Precision Recursive Block Diagonalization for Bivariate Functions of Matrices ⋮ Calculating a function of a matrix with a real spectrum ⋮ Low-rank tensor structure preservation in fractional operators by means of exponential sums ⋮ Limited‐memory polynomial methods for large‐scale matrix functions ⋮ Sensitivity of Matrix Function Based Network Communicability Measures: Computational Methods and A Priori Bounds ⋮ A Unifying Framework for Higher Order Derivatives of Matrix Functions ⋮ The Fréchet derivative of the tensor t-function ⋮ Norm and Trace Estimation with Random Rank-one Vectors ⋮ Integral representations for higher-order Fréchet derivatives of matrix functions: quadrature algorithms and new results on the level-2 condition number

Uses Software

• Algorithm 432

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices
• Approximation of functions of large matrices with Kronecker structure
• Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices
• From quantum to classical molecular dynamics: Reduced models and numerical analysis.
• Fields of values and the ADI method for non-normal matrices
• Computationally enhanced projection methods for symmetric Sylvester and Lyapunov matrix equations
• Balanced truncation model order reduction in limited time intervals for large systems
• Block Krylov subspace methods for functions of matrices
• Sparse solution of the Lyapunov equation for large-scale interconnected systems
• On the numerical solution of \(AX-XB=C\)
• Matrix Algorithms
• Frequency-Limited Balanced Truncation with Low-Rank Approximations
• Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
• Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: a state of the art survey
• Model reduction in limited time and frequency intervals
• Krylov Subspace Methods for Linear Systems with Tensor Product Structure
• Error Estimates and Evaluation of Matrix Functions via the Faber Transform
• Norm estimates for functions of two non-commuting matrices
• An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation
• Computational Methods for Linear Matrix Equations
• Convergence Analysis of Projection Methods for the Numerical Solution of Large Lyapunov Equations
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Numerical Methods for Large-Scale Lyapunov Equations with Symmetric Banded Data
• Low-Rank Updates and a Divide-And-Conquer Method for Linear Matrix Equations
• Oblique Production Methods for Large Scale Model Reduction
• A Chain Rule for Matrix Functions and Applications
• Bivariate matrix functions
• The Numerical Range is a $(1+\sqrt{2})$-Spectral Set
• Multivariate polynomial approximation in the hypercube
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Low-Rank Updates of Matrix Functions
• Functions of Matrices
• Explicit Solutions of Linear Matrix Equations

This page was built for publication: A Krylov Subspace Method for the Approximation of Bivariate Matrix Functions