Related papers: Creative Telescoping for Hypergeometric Double Sum…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…
We present here algorithms for efficient computation of linear algebra problems over finite fields.
A solution to the effectiveness problem in Kohn's algorithm for generating subelliptic multipliers is provided for domains that include those given by sums of squares of holomorphic functions (also including infinite sums). These domains…
The double sum sum_(j=0)^m sum_(i=0)^j (-1)^(j-i) C(m,j) C(j,i) C(j+k+qi,j+k) with free nonnegative integer parameters k and q is rewritten as hypergeometric series. Efficient formulas to generate the C-finite ordinary generating functions…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane…
Several new identities for elliptic hypergeometric series are proved. Remarkably, some of these are elliptic analogues of identities for basic hypergeometric series that are balanced but not very-well-poised.
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…
The search for linguistic patterns, stylometry and forensic linguistics have in the theory of complex networks, their structures and associated mathematical tools, allies with which to model and analyze texts. In this paper we present a new…
The main aim of this work is to derive the $q$-recurrence relations, $q$-partial derivative relations and summation formula of bibasic Humbert hypergeometric function $\Phi_1$ on two independent bases $q$ and $q_{1}$ of two variables and…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
Parameterized telescoping (including telescoping and creative telescoping) and refined versions of it play a central role in the research area of symbolic summation. Karr introduced 1981 $\Pi\Sigma$-fields, a general class of difference…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the…
Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…