Matrix arithmetic-geometric mean and the computation of the logarithm
JR Cardoso, R Ralha - SIAM Journal on Matrix Analysis and Applications, 2016 - SIAM
We investigate the stability of the matrix arithmetic-geometric mean (AGM) iteration. We
show that the classical formulation of this iteration may be not stable (a necessary and …
show that the classical formulation of this iteration may be not stable (a necessary and …
Multiprecision algorithms for computing the matrix logarithm
Two algorithms are developed for computing the matrix logarithm in floating point arithmetic
of any specified precision. The backward error-based approach used in the state of the art …
of any specified precision. The backward error-based approach used in the state of the art …
Computing the weighted geometric mean of two large-scale matrices and its inverse times a vector
M Fasi, B Iannazzo - SIAM Journal on Matrix Analysis and Applications, 2018 - SIAM
We investigate different approaches for computing the action of the weighted geometric
mean of two large-scale positive definite matrices on a vector. We derive and analyze …
mean of two large-scale positive definite matrices on a vector. We derive and analyze …
The geometric mean of two matrices from a computational viewpoint
B Iannazzo - Numerical Linear Algebra with Applications, 2016 - Wiley Online Library
The geometric mean of two matrices is considered from a computational viewpoint. Several
numerical algorithms based on different properties and representations of the geometric …
numerical algorithms based on different properties and representations of the geometric …
Computing the Fréchet derivative of the matrix logarithm and estimating the condition number
The most popular method for computing the matrix logarithm is the inverse scaling and
squaring method, which is the basis of the recent algorithm of Al-Mohy and Higham [SIAM J …
squaring method, which is the basis of the recent algorithm of Al-Mohy and Higham [SIAM J …
A new scaling and squaring algorithm for the matrix exponential
AH Al-Mohy, NJ Higham - SIAM Journal on Matrix Analysis and Applications, 2010 - SIAM
The scaling and squaring method for the matrix exponential is based on the approximation
e^A≈(r_m(2^-sA))^2^s, where r_m(x) is the m/m Padé approximant to e^x and the integers …
e^A≈(r_m(2^-sA))^2^s, where r_m(x) is the m/m Padé approximant to e^x and the integers …
Computing the Fréchet derivative of the matrix logarithm and estimating the condition number
The most popular method for computing the matrix logarithm is the inverse scaling and
squaring method, which is the basis of the recent algorithm of [AH Al-Mohy and NJ …
squaring method, which is the basis of the recent algorithm of [AH Al-Mohy and NJ …
The two-stage arithmetic mean method
E Galligani, V Ruggiero - Applied Mathematics and Computation, 1997 - Elsevier
In several recent works, the Arithmetic Mean Method for solving large sparse linear systems
has been introduced and analysed. Each iteration of this method consists of solving two …
has been introduced and analysed. Each iteration of this method consists of solving two …
Approximating the logarithm of a matrix to specified accuracy
The standard inverse scaling and squaring algorithm for computing the matrix logarithm
begins by transforming the matrix to Schur triangular form in order to facilitate subsequent …
begins by transforming the matrix to Schur triangular form in order to facilitate subsequent …
Computing the Matrix Logarithm with the Romberg Integration Method
The matrix logarithm function has applicability in many engineering and science fields.
Improvements in its calculation, from the point of view of both accuracy and/or execution …
Improvements in its calculation, from the point of view of both accuracy and/or execution …