Related papers: Efficient Computation of a Canonical Form for a Ge…
Formulas to calculate multivector exponentials in a base-free representation and in a orthonormal basis are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on the analysis of roots of characteristic…
The Canonical Polyadic decomposition (CPD) is a convenient and intuitive tool for tensor factorization; however, for higher-order tensors, it often exhibits high computational cost and permutation of tensor entries, these undesirable…
Finding a common factor of two multivariate polynomials with approximate coefficients is a problem in symbolic-numeric computing. Taking a tropical view on this problem leads to efficient preprocessing techniques, applying polyhedral…
The problem of finding a canonical form of complex matrices up to conjugacy with the set of canonical matrices being a union of affine planes in the matrix space is considered. A solution of the problem is given producing a new canonical…
Gradient-based algorithms, popular strategies to optimization problems, are essential for many modern machine-learning techniques. Theoretically, extreme points of certain cost functions can be found iteratively along the directions of the…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
The aim of this paper is to start the study of images of graded polynomials on full matrix algebras. We work with the matrix algebra $M_n(K)$ over a field $K$ endowed with its canonical $\mathbb{Z}_n$-grading (Vasilovsky's grading). We…
A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different…
In this paper polynomial maps are represented by the use of matrices whose entries are numbered by pair of multiindices and a new product of such matrices is introduced. A matrix representation of composition of polynomial maps is given. In…
We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…
We study the decomposition of multivariate polynomials as sums of powers of linear forms. As one of our main results we give an algorithm for the following problem: given a homogeneous polynomial of degree 3, decide whether it can be…
We propose a framework for fitting fractional polynomials models as special cases of Bayesian Generalized Nonlinear Models, applying an adapted version of the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…
New geometric methods for fast evaluation of derivatives of polynomial and rational B\'{e}zier curves are proposed. They apply an algorithm for evaluating polynomial or rational B\'{e}zier curves, which was recently given by the authors.…
A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…
We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime $p$. In particular, in the integer case, we improve a recent bound…
We present a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves and are useful in many aspects of computational number theory and cryptography. Our…