We consider the two logarithmic strain measures=||\mathrm dev _n\mathrm log U||=||\mathrm
dev _n\mathrm log F^ TF||\quad and\quad\vol=|\mathrm tr (\mathrm log U)=|\mathrm tr …

In this paper we present a survey of various algorithms for computing matrix geometric
means and derive new second-order optimization algorithms to compute the Karcher mean …

We investigate a family of isotropic volumetric-isochoric decoupled strain energies F ↦ W_
eH (F):= W _ eH (U):=\left {μ ke^ k ‖ dev _n U ‖^ 2+ κ 2 ke^ k tr (\log U)^ 2 & if\det F> …

This short note provides an explicit description of the Fréchet derivatives of the principal
square root matrix function at any order. We present an original formulation that allows to …

The Schur--Padé algorithm NJ Higham and L. Lin, SIAM J. Matrix Anal. Appl., 32 (2011), pp.
1056--1078 computes arbitrary real powers A^t of a matrix A∈C^n*n using the building …

A matrix is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set
of nondiagonalizable matrices has measure zero, every is the limit of diagonalizable …

Several existing algorithms for computing the matrix cosine employ polynomial or rational
approximations combined with scaling and use of a double angle formula. Their derivations …

We propose a method for model reduction on a given frequency range, without the use of
input and output filter weights. The method uses a nonlinear optimization approach to …

In the field of signal processing, the sampling theorem plays a fundamental role for signal
reconstruction as it bridges the gap between analog and digital signals. Following the …

A few matrix-vector multiplications with random vectors are often sufficient to obtain
reasonably good estimates for the norm of a general matrix or the trace of a symmetric …