A Unifying Framework for Higher Order Derivatives of Matrix Functions
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Publication:6154954
DOI10.1137/23m1580589arXiv2306.15814OpenAlexW4391647040WikidataQ128381764 ScholiaQ128381764MaRDI QIDQ6154954
Publication date: 16 February 2024
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2306.15814
Fréchet derivativepartial derivativequantum perturbation theorymatrix functioncomplex step approximationDaleckiĭ-Kreĭn formula
Cites Work
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- The complex step approximation to the Fréchet derivative of a matrix function
- The rank of powers of matrices in a block triangular form
- Evaluating the Fréchet derivative of the matrix exponential
- Derivatives of the matrix exponential and their computation
- The complex step approximation to the higher order Fréchet derivatives of a matrix function
- Integral representations for higher-order Fréchet derivatives of matrix functions: quadrature algorithms and new results on the level-2 condition number
- Evaluating the Fréchet derivative of the matrix \(p\)th root
- Explicit functional calculus
- Bounds for the spectral norm of functions of matrices
- Characterization of analytic functions in Banach spaces
- Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number
- Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number
- Using Multicomplex Variables for Automatic Computation of High-Order Derivatives
- A Krylov Subspace Method for the Approximation of Bivariate Matrix Functions
- Eigenvalue neutrality in block triangular matrices
- 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 Index and the Drazin Inverse of Block Triangular Matrices
- Using Complex Variables to Estimate Derivatives of Real Functions
- Condition Estimates for Matrix Functions
- On the Index of Block Upper Triangular Matrices
- Condition Estimation for Matrix Functions via the Schur Decomposition
- A Chain Rule for Matrix Functions and Applications
- Computing low‐rank approximations of the Fréchet derivative of a matrix function using Krylov subspace methods
- A Formula for the Fréchet Derivative of a Generalized Matrix Function
- Functions Preserving Matrix Groups and Iterations for the Matrix Square Root
- The Scaling and Squaring Method for the Matrix Exponential Revisited
- A Block Krylov Method to Compute the Action of the Fréchet Derivative of a Matrix Function on a Vector with Applications to Condition Number Estimation
- Functions of Matrices
- The complex-step derivative approximation
- Some Remarks on Variations and Differentials
- Integration and differentiation of functions of Hermitian operators and applications to the theory of perturbations
- Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative
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