Matrix Arithmetic-Geometric Mean and the Computation of the Logarithm

DOI10.1137/140998226zbMath1338.65121OpenAlexW2415101657MaRDI QIDQ2813335

Rui Ralha, João R. Cardoso

Publication date: 23 June 2016

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1822/42071

zbMATH Keywords

stabilityconvergencematrix square rootFréchet derivativeelliptic integralsmatrix logarithmarithmetic-geometric mean iteration

Mathematics Subject Classification ID

Related Items (3)

Multiprecision Algorithms for Computing the Matrix Logarithm ⋮ Algorithms for the computation of the matrix logarithm based on the double exponential formula ⋮ Conditioning of the matrix-matrix exponentiation

Uses Software

• Matlab
• mctoolbox
• mftoolbox

Cites Work

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• The arithmetic-geometric mean of Gauss
• The matrix sign function and computations in systems
• Stable iterations for the matrix square root
• Positive definite matrices
• Convergence of the arithmetic-geometric mean procedure for the complex variables and the calculation of the complete elliptic integrals with complex modulus
• Approximating the Logarithm of a Matrix to Specified Accuracy
• Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number
• Aggressively Truncated Taylor Series Method for Accurate Computation of Exponentials of Essentially Nonnegative Matrices
• Modern Computer Arithmetic
• Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm
• The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions
• FAST COMPUTATION OF MATRIX EXPONENTIAL AND LOGARITHM
• AN ALGORITHM FOR FAST HIGH PRECISION COMPUTATION OF MATRIX EXPONENTIAL AND LOGARITHM
• Arithmetic-geometric means of positive matrices
• Fast Multiple-Precision Evaluation of Elementary Functions
• Condition Estimates for Matrix Functions
• Successive iterations and logarithmic means
• Functions Preserving Matrix Groups and Iterations for the Matrix Square Root
• Functions of Matrices

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