Generalized integrating factor methods for stiff PDEs
Journal of Computational Physics
Padé and Gregory error estimates for the logarithm of block triangular matrices
Applied Numerical Mathematics
Journal of Computational Physics
The solution of s exp(s) = a is not always the lambert w function of a
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Algorithm 894: On a block Schur--Parlett algorithm for ϕ-functions based on the sep-inverse estimate
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics
Padé and Gregory error estimates for the logarithm of block triangular matrices
Applied Numerical Mathematics
Prospectus for the next LAPACK and ScaLAPACK libraries
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
A New Scaling and Squaring Algorithm for the Matrix Exponential
SIAM Journal on Matrix Analysis and Applications
On the use of matrix functions for fractional partial differential equations
Mathematics and Computers in Simulation
Technical communique: Frequency-truncated system norms
Automatica (Journal of IFAC)
Steady affine motions and morphs
ACM Transactions on Graphics (TOG)
Schur decomposition methods for the computation of rational matrix functions
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part IV
Computing matrix functions solving coupled differential models
Mathematical and Computer Modelling: An International Journal
Computing matrix functions using mixed interpolation methods
Mathematical and Computer Modelling: An International Journal
Lie-group interpolation and variational recovery for internal variables
Computational Mechanics
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An algorithm for computing matrix functions is presented. It employs a Schur decomposition with reordering and blocking followed by the block form of a recurrence of Parlett, with functions of the nontrivial diagonal blocks evaluated via a Taylor series. A parameter is used to balance the conflicting requirements of producing small diagonal blocks and keeping the separations of the blocks large. The algorithm is intended primarily for functions having a Taylor series with an infinite radius of convergence, but it can be adapted for certain other functions, such as the logarithm. Novel features introduced here include a convergence test that avoids premature termination of the Taylor series evaluation and an algorithm for reordering and blocking the Schur form. Numerical experiments show that the algorithm is competitive with existing special-purpose algorithms for the matrix exponential, logarithm, and cosine. Nevertheless, the algorithm can be numerically unstable with the default choice of its blocking parameter (or in certain cases for all choices), and we explain why determining the optimal parameter appears to be a very difficult problem. A MATLAB implementation is available that is much more reliable than the function funm in MATLAB 6.5 (R13).