Related papers: Products of Ordinary Differential Operators by Eva…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
An algorithm for matrix factorization of polynomials was proposed in \cite{fomatati2022tensor} and it was shown that this algorithm produces better results than the standard method for factoring polynomials on the class of summand-reducible…
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict…
Different possible sources are discussed for enhancement of the calculation time when solving ordinary differential equations systems to forecast space objects' motion. This paper presents an approach for building an integrator of ordinary…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the…
The problem of straggler mitigation in distributed matrix multiplication (DMM) is considered for a large number of worker nodes and a fixed small finite field. Polynomial codes and matdot codes are generalized by making use of algebraic…
The operator product expansion is used to compute the matrix elements of composite renormalized operators on the lattice. We study the product of two fundamental fields in the two-dimensional sigma-model and discuss the possible sources of…
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…
Model Order Reduction is a key technology for industrial applications in the context of digital twins. Key requirements are non-intrusiveness, physics-awareness, as well as robustness and usability. Operator inference based on least-squares…
For the case of a relativistic scalar field at finite temperature with a chemical potential, we calculate an exact expression for the one-loop effective action using the full fourth order determinant and zeta-function regularisation. We…
The overlap Dirac operator at nonzero quark chemical potential involves the computation of the sign function of a non-Hermitian matrix. In this talk we present an iterative method, first proposed by us in Ref. [1], which allows for an…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. As opposed to binary matrix factorization which uses standard arithmetic, BMF uses the Boolean OR and Boolean AND…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a…
In recent years, with the rapid development of electro-optic modulators, optical computing has become a potential excellent candidate for various computing tasks. New structures and devices for optical computing are emerging one after…
The article presents a matrix differential operator and a pseudoinverse matrix differential operator for finding a particular solution to nonhomogeneous linear ordinary differential equations (ODE) with constant coefficients with special…
We introduce a class of iterated logarithmic Lipschitz spaces $\mathcal{L}^{(k)}$, $k\in\mathbb{N}$, on an infinite tree which arise naturally in the context of operator theory. We characterize boundedness and compactness of the…
We show that any scalar differential operator with a family of polyno- mials as its common eigenfunctions leads canonically to a matrix differen- tial operator with the same property. The construction of the correspond- ing family of matrix…
Below the normalized weighted reciprocal of the Christoffel function with respect to exceptional Jacobi polynomials is investigated. It is proved that it tends to the equilibrium measure of the interval of orthogonality in weak-star sense.…