Related papers: Fast Symbolic Integer-Linear Spectra
The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both…
In this work we show how auxiliary variables can be used to give an efficient method involving symbolic manipulation and Picard iteration for approximating solutions of certain Volterra integral equations.
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…
A symbolic computational algorithm which detects " linear "` solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
In latest years, several advancements have been made in symbolic-numerical eigenvalue techniques for solving polynomial systems. In this article, we add to this list. We design an algorithm which solves systems with isolated solutions…
State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important…
The development of advanced software tools for power system analysis requires extensive programming expertise. Even when using open-source tools, programming skills are essential to modify built-in models. This can be particularly…
Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
This paper presents a symbolic algorithm for solving band matrix systems of linear algebraic equations with heptadiagonal coefficient matrices. The algorithm is given in pseudocode. A theorem which gives the condition for the algorithm to…
This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space $x$ and frequency $\xi$. The symbol smoothness conditions obeyed by many…
We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the…
Hermitian linear matrix pencils are ubiquitous in control theory, operator systems, semidefinite optimization, and real algebraic geometry. This survey reviews the fundamental features of the matricial solution set of a linear matrix…
The ability to decompose a signal in an orthonormal basis (a set of orthogonal components, each normalized to have unit length) using a fast numerical procedure rests at the heart of many signal processing methods and applications. The…
In some real world situations, linear models are not sufficient to represent accurately complex relations between input variables and output variables of a studied system. Multilayer Perceptrons are one of the most successful non-linear…
We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we…
Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary…
A recent trend in probabilistic inference emphasizes the codification of models in a formal syntax, with suitable high-level features such as individuals, relations, and connectives, enabling descriptive clarity, succinctness and…
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…
We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…
Hyperbolic problems can at times be solved employing symbolic arguments. This is especially true for the construction of forward (and backward) fundamental solutions. We formulate a corresponding abstract scheme and illustrate its…