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Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…

Numerical Analysis · Mathematics 2022-04-11 Kai Diethelm

We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…

Symbolic Computation · Computer Science 2011-03-25 Eric Berberich , Pavel Emeliyanenko , Alexander Kobel , Michael Sagraloff

For linear operators which factor with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same…

Commutative Algebra · Mathematics 2007-05-23 A. Rod Gover , Josef Silhan

The Integral Image algorithm is often applied in tasks that require efficient integration over images, such as object detection. In this paper we discuss theoretical aspects of the algorithm's continuous version. We suggest to define the…

Discrete Mathematics · Computer Science 2015-03-17 Amir Shachar

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…

Algebraic Geometry · Mathematics 2010-08-24 Yong Feng , Wenyuan Wu , Jingzhong Zhang

We present a new algorithm to decompose generic spinor polynomials into linear factors. Spinor polynomials are certain polynomials with coefficients in the geometric algebra of dimension three that parametrize rational conformal motions.…

Rings and Algebras · Mathematics 2023-11-14 Zijia Li , Hans-Peter Schröcker , Johannes Siegele

We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…

Logic in Computer Science · Computer Science 2014-10-06 David Monniaux , Peter Schrammel

A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…

Mathematical Physics · Physics 2009-11-11 J. A. Calzada , J. Negro , M. A. del Olmo

Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…

Artificial Intelligence · Computer Science 2015-05-19 Toby Walsh

By analytically continuing QCD scattering amplitudes through specific complexified momenta, one can study and learn about the nature and the consequences of factorization and unitarity. In some cases, when coupled with the largest time…

High Energy Physics - Theory · Physics 2008-11-26 Diana Vaman , York-Peng Yao

We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly…

Numerical Analysis · Mathematics 2022-05-10 Stefano De Marchi , Nadaniela Egidi , Josephin Giacomini , Pierluigi Maponi , Alessia Perticarini

In our previous works (2012, 2013), we provided a finite list of properties characterizing all potential types of quadratic birational transformations of a projective space into a factorial variety, whose base locus is smooth and…

Algebraic Geometry · Mathematics 2015-12-01 Giovanni Staglianò

We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…

Numerical Analysis · Mathematics 2013-12-31 Na Li , Carmeliza Navasca

Formulating a Schubert problem as the solutions to a system of equations in either Pl\"ucker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously…

Algebraic Geometry · Mathematics 2015-07-09 Nickolas Hein , Frank Sottile

We consider polynomials of bi-degree $(n,1)$ over the skew field of quaternions where the indeterminates commute with each other and with all coefficients. Polynomials of this type do not generally admit factorizations. We recall a…

Rings and Algebras · Mathematics 2022-02-21 Johanna Lercher , Daniel F. Scharler , Hans-Peter Schröcker , Johannes Siegele

We identify and analyse obstructions to factorisation of integer matrices into products $N^T N$ or $N^2$ of matrices with rational or integer entries. The obstructions arise as quadratic forms with integer coefficients and raise the…

Number Theory · Mathematics 2021-03-09 Nicholas J. Higham , Matthew C. Lettington , Karl Michael Schmidt

An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively…

Computational Physics · Physics 2023-04-19 Johan Lundgren , Kurt Schab , Miloslav Capek , Mats Gustafsson , Lukas Jelinek

Lifted probabilistic inference exploits symmetries in a probabilistic model to allow for tractable probabilistic inference with respect to domain sizes. To apply lifted inference, a lifted representation has to be obtained, and to do so,…

Artificial Intelligence · Computer Science 2023-12-18 Malte Luttermann , Tanya Braun , Ralf Möller , Marcel Gehrke

Individual scores on common factors are required in some applied settings (e.g., business and marketing settings). Common factors are based on reflective indicators, but their scores cannot unambiguously be determined. Therefore, factor…

Applications · Statistics 2017-01-24 André Beauducel , Anja Leue , Norbert Hilger

Chordal and factor-width decomposition methods for semidefinite programming and polynomial optimization have recently enabled the analysis and control of large-scale linear systems and medium-scale nonlinear systems. Chordal decomposition…

Optimization and Control · Mathematics 2021-11-23 Yang Zheng , Giovanni Fantuzzi , Antonis Papachristodoulou