Related papers: A Variant of Gerdt's Algorithm for Computing Invol…
In this work we study five Grovers algorithm modifications, where each iteration is constructed by two generalized Householder reflections, against inaccuracies in the phases. By using semi-empirical methods, we investigate various…
Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been…
Solving zero-dimensional polynomial systems using Gr\"obner bases is usually done by, first, computing a Gr\"obner basis for the degree reverse lexicographic order, and next computing the lexicographic Gr\"obner basis with a change of order…
Many algorithms and applications involve repeatedly solving variations of the same inference problem; for example we may want to introduce new evidence to the model or perform updates to conditional dependencies. The goal of adaptive…
Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field. Consider a field $K = \mathbb{Q}(\alpha)$, a…
Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…
An algorithm to generate a minimal comprehensive Gr\"obner\, basis of a parametric polynomial system from an arbitrary faithful comprehensive Gr\"obner\, system is presented. A basis of a parametric polynomial ideal is a comprehensive…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
General revision. In particular the parts concerning involutive bases over rings have been significantly changed. In addition some proofs have been improved.
We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…
The translation of Grover's search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are…
Subject of this paper is an implementation of a well-known Motzkin-Burger algorithm, which solves the problem of finding the full set of solutions of a system of linear homogeneous inequalities. There exist a number of implementations of…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a…
Matrix operations such as matrix inversion, eigenvalue decomposition, singular value decomposition are ubiquitous in real-world applications. Unfortunately, many of these matrix operations so time and memory expensive that they are…
We present a general scheme for the construction of new eficient generalized Schultz iterative methods for computing the inverse matrix. These methods have the form $$ X_{k+1} = X_k(a_0^{(k)}I+a_1^{(k)}AX_k),\quad k\in\mathbb{N}, $$ where…
The objective of this publication is to reduce the sensitivity of iterative equation solvers on the initial value. To this end, at the hand of Newton's method, we exemplify how to reformulate the initial problem by means of a set of…
A modification of Grover's algorithm is proposed, which can be used directly as a fast database search. An explicit two q-bit example is displayed in detail. We discuss the case where the database has multiple entries corresponding to the…
Over the past decade, the Gr\"obner basis theory and automatic solver generation have lead to a large number of solutions to geometric vision problems. In practically all cases, the derived solvers apply a fixed elimination template to…
Opportunity cost matrices are interesting in the context of scenario reduction. We provide new algorithms, based on ideas from algebraic geometry, to efficiently compute the opportunity cost matrix using computational algebraic geometry. We…