Journal ArticleDOI
Nineteen Dubious Ways to Compute the Exponential of a Matrix
Cleve B. Moler,Charles Van Loan +1 more
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In this article, the exponential of a matrix could be computed in many ways, including approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial.Abstract:
In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polyn...read more
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Journal ArticleDOI
IQ-TREE 2: New Models and Efficient Methods for Phylogenetic Inference in the Genomic Era.
Bui Quang Minh,Heiko A. Schmidt,Olga Chernomor,Dominik Schrempf,Dominik Schrempf,Michael D. Woodhams,Arndt von Haeseler,Arndt von Haeseler,Robert Lanfear +8 more
TL;DR: Some notable features of IQ-TREE version 2 are described and the key advantages over other software are highlighted.
Book
Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems
TL;DR: This book discusses infinite difference approximations, Iterative methods for sparse linear systems, and zero-stability and convergence for initial value problems for ordinary differential equations.
Journal ArticleDOI
New results on the single server queue with a batch markovian arrival process
TL;DR: This work generalizes results to the single server queue with the batch arrival process and emphasizes the resulting simplifications of the computational complexity of the algorithmic solution of single server queues with a general Markovian arrival process.
Journal ArticleDOI
The Magnus expansion and some of its applications
TL;DR: Magnusson expansion as discussed by the authors provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory (TEPT).
Journal ArticleDOI
A likelihood approach for comparing synonymous and nonsynonymous nucleotide substitution rates, with application to the chloroplast genome.
Spencer V. Muse,Brandon S. Gaut +1 more
TL;DR: Simulations help confirm previous suggestions that silent sites are saturated, leaving no evidence of heterogeneity in synonymous substitution rates, and confirm previous findings that substitution rates in the chloroplast genome are subject to both lineage-specific and locus-specific effects.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.