On the Matrix Mittag–Leffler Function: Theoretical Properties and Numerical Computation

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Numerical Computation of Matrix Functions

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On the Numerical Computation of the Matrix Exponential

Random Matrix Theory, Numerical Computation and Applications

This paper serves to prove the thesis that a computational trick can open entirely new approaches to theory. We illustrate by describing such random matrix techniques as the stochastic operator approach, the method of ghosts and shadows, and the method of “Riccatti Diffusion/Sturm Sequences,” giving new insights into the deeper mathematics underneath random matrix theory.

Entropic Affinities: Properties and Efficient Numerical Computation

Gaussian affinities are commonly used in graph-based methods such as spectral clustering or nonlinear embedding. Hinton and Roweis (2003) introduced a way to set the scale individually for each point so that it has a distribution over neighbors with a desired perplexity, or effective number of neighbors. This gives very good affinities that adapt locally to the data but are harder to compute. W...