Related papers: Computing the Mittag-Leffler Function of a Matrix …
The bilinear form of a matrix function, namely $\mathbf{u}^\top f(A) \mathbf{v}$, appears in many scientific computing problems, where $\mathbf{u}, \mathbf{v} \in \mathbb{R}^n$, $A \in \mathbb{R}^{n \times n}$, and $f(z)$ is a given…
Solution of fractional differential equations is an emerging area of present day research because such equations arise in various applied fields. In this paper we have developed analytical method to solve the system of fractional…
Numeric modeling of electromagnetics and acoustics frequently entails matrix-vector multiplication with block Toeplitz structure. When the corresponding block Toeplitz matrix is not highly sparse, e.g. when considering the electromagnetic…
We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factorization. We prove there is a Schur factorization for commuting…
This paper presents the first model-checking algorithm for an expressive modal mu-calculus over timed automata, $L^{\mathit{rel}, \mathit{af}}_{\nu,\mu}$, and reports performance results for an implementation. This mu-calculus contains…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
We survey a number of different methods for computing $L(\chi,1-k)$ for a Dirichlet character $\chi$, with particular emphasis on quadratic characters. The main conclusion is that when $k$ is not too large (for instance $k\le100$) the best…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…
Matrix Factorization (MF) has found numerous applications in Machine Learning and Data Mining, including collaborative filtering recommendation systems, dimensionality reduction, data visualization, and community detection. Motivated by the…
The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log 2 (7) $\approx$ 2.8074.…
In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative…
We present new algorithms that efficiently approximate the hypergeometric function of a matrix argument through its expansion as a series of Jack functions. Our algorithms exploit the combinatorial properties of the Jack function, and have…
Pre-trained machine learning (ML) predictions have been increasingly used to complement incomplete data to enable downstream scientific inquiries, but their naive integration risks biased inferences. Recently, multiple methods have been…
In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…
A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine…
This work is the second installment of a series on the loop-string-hadron (LSH) approach to SU(3) lattice Yang-Mills theory. Here, we present the infinite-dimensional matrix representation for arbitrary gauge-invariant operators at a…
A DualTPD method is proposed for solving nonlinear partial differential equations. The method is characterized by three main features. First, decoupling via Fenchel--Rockafellar duality is achieved, so that nonlinear terms are discretized…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
A shift-invariant system is a collection of functions $\{g_{m,n}\}$ of the form $g_{m,n}(k) = g_m(k-an)$. Such systems play an important role in time-frequency analysis and digital signal processing. A principal problem is to find a dual…
Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We…