Search results for "Hilbert matrix"

showing 2 items of 2 documents

Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces

2007

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…

Hilbert manifoldHilbert's basis theoremHilbert matrix01 natural sciencesMathematics - Algebraic Geometrysymbols.namesakeCharacteristic classesPrimary 14C05Secondary 14C170103 physical sciencesFOS: Mathematics[MATH]Mathematics [math]0101 mathematicsAlgebraic Geometry (math.AG)ComputingMilieux_MISCELLANEOUSMathematicsHilbert–Poincaré seriesHilbert's second problemHilbert series and Hilbert polynomialAlgebra and Number Theory010102 general mathematicsHilbert's fourteenth problemUniversal formulasPrimary 14C05; Secondary 14C17Hilbert schemes of pointsAlgebraHilbert schemesymbols[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physics
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Diagonalization of large matrices: a new parallel algorithm.

2015

On the basis of a dressed matrices formalism, a new algorithm has been devised for obtaining the lowest eigenvalue and the corresponding eigenvector of large real symmetric matrices. Given an N × N matrix, the proposed algorithm consists in the diagonalization of (N - 1)2 × 2 dressed matrices. Both sequential and parallel versions of the proposed algorithm have been implemented. Tests have been performed on a Hilbert matrix, and the results show that this algorithm is up 340 times faster than the corresponding LAPACK routine for N = 10(4) and about 10% faster than the Davidson method. The parallel MPI version has been tested using up to 512 nodes. The speed-up for a N = 10(6) matrix is fair…

Mathematical analysisParallel algorithmHilbert matrixComputer Science ApplicationsOrthogonal diagonalizationsymbols.namesakeMatrix (mathematics)symbolsSymmetric matrixPhysical and Theoretical ChemistryGround stateWave functionEigenvalues and eigenvectorsMathematicsJournal of chemical theory and computation
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