Related papers: Computing differential subresultants with Maple
This paper is concerned with computations of a few smaller eigenvalues (in absolute value) of a large extremely ill-conditioned matrix. It is shown that smaller eigenvalues can be accurately computed for a diagonally dominant matrix or a…
In this article we obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and quasiperiodic boundary conditions. Then using these…
We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…
We present the Maple package TDDS (Thomas Decomposition of Differential Systems). Given a polynomially nonlinear differential system, which in addition to equations may contain inequations, this package computes a decomposition of it into a…
In this paper we construct examples of commuting ordinary scalar differential operators with polynomial coefficients that are related to a spectral curve of an arbitrary genus g>0 and to an arbitrary rank r>1 of the vector bundle of common…
Computer algebra procedures to manipulate pseudo-differential operators are implemented to perform calculations with integrable models. We use lazy evaluation and streams to represent and operate with pseudo-differential operators. No order…
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the…
In this paper we study self-adjoint commuting ordinary differential operators with polynomial coefficients. These operators define commutative subalgebras of the first Weyl algebra. We find new examples of commuting operators of rank 2.
A Maple package for computing Groebner bases of linear difference ideals is described. The underlying algorithm is based on Janet and Janet-like monomial divisions associated with finite difference operators. The package can be used, for…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…
The assessment of regression models with discrete outcomes is challenging and has many fundamental issues. With discrete outcomes, standard regression model assessment tools such as Pearson and deviance residuals do not follow the…
We introduce the Macaulay2 package SparseResultants, which provides general tools for computing sparse resultants, sparse discriminants, and hyperdeterminants. We give some background on the theory and briefly show how the package works.
In this paper we discuss some results related to commuting ordinary differential operators of rank greater than one.
Algorithmic differentiation (AD) tools allow to obtain gradient information of a continuously differentiable objective function in a computationally cheap way using the so-called backward mode. It is common practice to use the same tools…
We suggest a new concept of functional-differential operators with constant delay on geometrical graphs that involves {\it global} delay parameter. Differential operators on graphs model various processes in many areas of science and…
Semidefinite programs are an important class of convex optimization problems. It can be solved efficiently by SDP solvers in Matlab, such as SeDuMi, SDPT3, DSDP. However, since we are running fixed precision SDP solvers in Matlab, for some…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
To supplement the already known classification of traces on classical pseudodifferential operators, we present a classification of traces on the algebras of odd-class pseudodifferential operators of non-positive order acting on smooth…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
Determinantal point processes (DPPs) are popular probabilistic models that arise in many machine learning tasks, where distributions of diverse sets are characterized by matrix determinants. In this paper, we develop fast algorithms to find…