Search results for "Numerical"

showing 10 items of 2002 documents

First-order expressibility of languages with neutral letters or: The Crane Beach conjecture

2005

A language L over an alphabet A is said to have a neutral letter if there is a letter [email protected]?A such that inserting or deleting e's from any word in A^* does not change its membership or non-membership in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first-order logic with linear order, then it is not definable in first-order logic with any set N of numerical predicates. Named after the location of its first, flawed, proof this conjecture is called the Crane Beach …

Discrete mathematicsConjectureComputer Networks and CommunicationsApplied MathematicsFirst orderNumerical predicatesPredicate (grammar)Theoretical Computer ScienceFirst-order logicIterated logarithmCombinatoricsComputational Theory and MathematicsRegular languageDatabase theoryCircuit complexityFirst-order logicCircuit uniformityMathematicsJournal of Computer and System Sciences
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Witness computation for solving geometric constraint systems

2014

International audience; In geometric constraint solving, the constraints are represented with an equation system F(U, X) = 0, where X denotes the unknowns and U denotes a set of parameters. The target solution for X is noted XT. A witness is a couple (U_W, X_W) such that F(U_W, X_W) = 0. The witness is not the target solution, but they share the same combinatorial features, even when the witness and the target lie on two distinct connected components of the solution set of F(U, X) = 0. Thus a witness enables the qualitative study of the system: the detection of over- and under-constrained systems, the decomposition into irreducible subsystems, the computation of subsystems boundaries. This …

Discrete mathematicsConnected componentMathematical optimization[ INFO ] Computer Science [cs]Numerical algorithmsComputer scienceComputationNumerical analysisSystem FSolution setBinary constraint[INFO] Computer Science [cs]16. Peace & justiceGeometric constraint solvingWitnessSimplex algorithmWitness computation[INFO]Computer Science [cs]
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Complete, Exact and Efficient Implementation for Computing the Adjacency Graph of an Arrangement of Quadrics

2007

The original publication is available at www.springerlink.com ; ISBN 978-3-540-75519-7 ; ISSN 0302-9743 (Print) 1611-3349 (Online); International audience; We present a complete, exact and efficient implementation to compute the adjacency graph of an arrangement of quadrics, \ie surfaces of algebraic degree~2. This is a major step towards the computation of the full 3D arrangement. We enhanced an implementation for an exact parameterization of the intersection curves of two quadrics, such that we can compute the exact parameter value for intersection points and from that the adjacency graph of the arrangement. Our implementation is {\em complete} in the sense that it can handle all kinds of…

Discrete mathematicsDegree (graph theory)ComputationDegenerate energy levelsACM: I.: Computing Methodologies/I.1: SYMBOLIC AND ALGEBRAIC MANIPULATION/I.1.2: Algorithms/I.1.2.0: Algebraic algorithms020207 software engineering010103 numerical & computational mathematics02 engineering and technology[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]01 natural sciencesACM: G.: Mathematics of Computing/G.4: MATHEMATICAL SOFTWARE/G.4.3: EfficiencyCombinatoricsIntersection0202 electrical engineering electronic engineering information engineeringGraph (abstract data type)Adjacency listGravitational singularity0101 mathematicsAlgebraic numberACM: G.: Mathematics of Computing/G.4: MATHEMATICAL SOFTWARE/G.4.0: Algorithm design and analysisMathematics
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Representation and factorization theorems for almost-Lp-spaces

2019

The first and fourth authors gratefully acknowledge the support of Ministerio de Ciencia, Innovacibn y Universidades (Spain), Agencia Estatal de Investigaciones, and FEDER, under projects MTM2014-53009-P (J.M. Calabuig) and MTM2016-77054-C2-1-P (E.A. Sanchez Perez).

Discrete mathematicsFactorizationGeneral MathematicsBanach lattice010102 general mathematicsRepresentation (systemics)010103 numerical & computational mathematics0101 mathematics01 natural sciencesMathematicsIndagationes Mathematicae
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A General Algorithm to Calculate the Inverse Principal $p$-th Root of Symmetric Positive Definite Matrices

2019

We address the general mathematical problem of computing the inverse p-th root of a given matrix in an efficient way. A new method to construct iteration functions that allow calculating arbitrary p-th roots and their inverses of symmetric positive definite matrices is presented. We show that the order of convergence is at least quadratic and that adaptively adjusting a parameter q always leads to an even faster convergence. In this way, a better performance than with previously known iteration schemes is achieved. The efficiency of the iterative functions is demonstrated for various matrices with different densities, condition numbers and spectral radii.

Discrete mathematicsMathematical problemPhysics and Astronomy (miscellaneous)Root (chord)InversePositive-definite matrixMathematics - Rings and AlgebrasNumerical Analysis (math.NA)01 natural sciences010101 applied mathematicsMatrix (mathematics)Quadratic equationRate of convergenceRings and Algebras (math.RA)Convergence (routing)FOS: MathematicsApplied mathematicsMathematics - Numerical Analysis0101 mathematicsMathematics
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On the optimal approximation rate of certain stochastic integrals

2010

AbstractGiven an increasing function H:[0,1)→[0,∞) and An(H)≔infτ∈Tn(∑i=1n∫ti−1ti(ti−t)H(t)2dt)12, where Tn≔{τ=(ti)i=0n:0=t0<t1<⋯<tn=1}, we characterize the property An(H)≤cn, and give conditions for An(H)≤cnβ and An(H)≥1cnβ for β∈(0,1), both in terms of integrability properties of H. These results are applied to the approximation of stochastic integrals.

Discrete mathematicsMathematics(all)Numerical AnalysisRegular sequencesGeneral MathematicsApplied MathematicsStochastic integralsNon linear approximationFunction (mathematics)CombinatoricsNon-linear approximationFunction compositionAnalysisMathematicsJournal of Approximation Theory
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Factorization of (q,p)-summing polynomials through Lorentz spaces

2017

[EN] We present a vector valued duality between factorable (q,p)-summing polynomials and (q,p)-summing linear operators on symmetric tensor products of Banach spaces. Several applications are provided. First, we prove a polynomial characterization of cotype of Banach spaces. We also give a variant of Pisier's factorization through Lorentz spaces of factorable (q,p)-summing polynomials from C(K)-spaces. Finally, we show a coincidence result for (q,p)-concave polynomials.(c) 2016 Elsevier Inc. All rights reserved.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsApplied MathematicsDiscrete orthogonal polynomials010102 general mathematicsBanach space010103 numerical & computational mathematics01 natural sciencesClassical orthogonal polynomialsDifference polynomialsFactorizationPisier's theoremWilson polynomialsOrthogonal polynomialsSymmetric tensorSumming polynomialsFactorization0101 mathematicsMATEMATICA APLICADAAnalysisMathematicsJournal of Mathematical Analysis and Applications
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P-matrix completions under weak symmetry assumptions

2000

An n-by-n matrix is called a Π-matrix if it is one of (weakly) sign-symmetric, positive, nonnegative P-matrix, (weakly) sign-symmetric, positive, nonnegative P0,1-matrix, or Fischer, or Koteljanskii matrix. In this paper, we are interested in Π-matrix completion problems, that is, when a partial Π-matrix has a Π-matrix completion. Here, we prove that a combinatorially symmetric partial positive P-matrix has a positive P-matrix completion if the graph of its specified entries is an n-cycle. In general, a combinatorially symmetric partial Π-matrix has a Π-matrix completion if the graph of its specified entries is a 1-chordal graph. This condition is also necessary for (weakly) sign-symmetric …

Discrete mathematicsMatrix completionNumerical AnalysisAlgebra and Number TheorySymmetric graphCombinatorial symmetry010102 general mathematicsComparability graphIncidence matrix010103 numerical & computational mathematics01 natural sciencesGraphCombinatoricsVertex-transitive graphP-matrixGraph powerDiscrete Mathematics and CombinatoricsRegular graphAdjacency matrixGeometry and Topology0101 mathematicsComplement graphMathematicsLinear Algebra and its Applications
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Domination spaces and factorization of linear and multilinear summing operators

2015

[EN] It is well known that not every summability property for multilinear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. Our construction includes the cases of absolutely p-summing linear operators, (p, sigma)-absolutely continuous linear operators, factorable strongly p-summing multilinear operators, (p(1), ... , p(n))-dominated multilinear operators and dominated (p(1), ... , p(n); sigma)-continuous multilinear operators.

Discrete mathematicsMultilinear mapPietsch's domination theoremMultilinear summing operators010102 general mathematicsMathematics::Classical Analysis and ODEs010103 numerical & computational mathematicsPietsch's domination theorem factorization of operators multilinear summing operators.Factorization of operators01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional AnalysisMathematics (miscellaneous)FactorizationFOS: Mathematics0101 mathematicsMATEMATICA APLICADAMathematics
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Certain subclasses of multivalent analytic functions defined by multiplier transforms

2010

By making use of the principle of subordination between analytic functions and a family of multiplier transforms, we introduce and investigate some new subclasses of multivalent analytic functions. Such results as inclusion relationships, subordination and superordination properties, integral-preserving properties, argument estimates and convolution properties are proved.

Discrete mathematicsMultiplier (Fourier analysis)Computational MathematicsPure mathematicsApplied MathematicsNumerical analysisAnalytic functionMathematicsApplied Mathematics and Computation
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