Testing Matrix Function Algorithms Using Identities

DOI10.1145/2723157zbMath1347.65087OpenAlexW1505874879WikidataQ56998607 ScholiaQ56998607MaRDI QIDQ2828165

Nicholas J. Higham, Edvin Deadman

Publication date: 24 October 2016

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: http://eprints.maths.manchester.ac.uk/2114/1/paper.pdf

zbMATH Keywords

testingMatlabmatrix functionbackward errorfunctional identityforward errornormwise relative error

Mathematics Subject Classification ID

Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items

Massively parallel sparse matrix function calculations with NTPoly, Estimating the condition number of \(f(A)b\), Testing Matrix Function Algorithms Using Identities, New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously, An Algorithm for the Matrix Lambert $W$ Function

Uses Software

• CELEFUNT
• LSQR
• Matlab
• NAG
• mctoolbox
• SciPy
• LSMR
• MATLAB expm
• mftoolbox
• CRAIG

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An augmented LSQR method
• The complex step approximation to the Fréchet derivative of a matrix function
• The matrix sign function and computations in systems
• Testing Matrix Function Algorithms Using Identities
• A Schur Logarithmic Algorithm for Fractional Powers of Matrices
• Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number
• An Improved Schur--Padé Algorithm for Fractional Powers of a Matrix and Their Fréchet Derivatives
• The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential
• Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number
• A Schur–Padé Algorithm for Fractional Powers of a Matrix
• LSMR: An Iterative Algorithm for Sparse Least-Squares Problems
• Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm
• A New Scaling and Squaring Algorithm for the Matrix Exponential
• Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• Algorithm 714: CELEFUNT: a portable test package for complex elementary functions
• A Schur Algorithm for Computing Matrix pth Roots
• A Schur-Parlett Algorithm for Computing Matrix Functions
• A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra
• Computational Techniques for Real Logarithms of Matrices
• Estimating the Condition Number of the Fréchet Derivative of a Matrix Function
• A Schur–Newton Method for the Matrix \lowercase{\boldmathp}th Root and its Inverse
• The Scaling and Squaring Method for the Matrix Exponential Revisited
• Functions of Matrices
• Some Remarks on Variations and Differentials
• A binary powering Schur algorithm for computing primary matrix roots