Related papers: On the bit-complexity of sparse polynomial multipl…
We introduce a method and an algorithm for computing the weighted Moore-Penrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are…
Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…
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.…
A method of fast linear transform algorithm synthesis for an arbitrary tensor, matrix, or vector is proposed. The method is based on factorization of a tensor and using the factors for building computational structures performing fast…
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…
In this paper, we give new sparse interpolation algorithms for black box polynomial f whose coefficients are from a finite set. In the univariate case, we recover f from one evaluation of f(a) for a sufficiently large number a. In the…
Fast algorithms for matrix multiplication, namely those that perform asymptotically fewer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few…
Achieving high efficiency with numerical kernels for sparse matrices is of utmost importance, since they are part of many simulation codes and tend to use most of the available compute time and resources. In addition, especially in large…
In this paper, we report on an implementation in the free software Mathemagix of lacunary factorization algorithms, distributed as a library called Lacunaryx. These algorithms take as input a polynomial in sparse representation, that is as…
We study the computational complexity of a diagonalization technique for multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear forms. It is based on Harrison's center theory and consists of a…
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
Factorization of polynomials is one of the foundations of symbolic computation. Its applications arise in numerous branches of mathematics and other sciences. However, the present advanced programming languages such as C++ and J++, do not…
In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
A purification algorithm for expanding the single-particle density matrix in terms of the Hamiltonian operator is proposed. The scheme works with a predefined occupation and requires less than half the number of matrix-matrix…
Supporting multiple partial computations efficiently at each of the workers is a keystone in distributed coded computing in order to speed up computations and to fully exploit the resources of heterogeneous workers in terms of…
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…
Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…