solving the subproblem in the lagrangian dual of separable discrete programs with linear constraints this note presents an efficient method for the routine solution of the subproblem associated with the lagrangian dual of discrete programming problems having separable non linear objective function and linear constraints an additional advantage for subgradient methods is described

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

on the evaluation of r chapman s evil determinant abstract we prove a conjecture of r chapman asserting that for any prime p 3 mod 4 the determinant of the p 1 2 p 1 2 matrix c c ij with c ji j i p is always 1

efficient solution of the simplified p n equations in this paper we show new solver strategies for the multigroup sp n equations for nuclear reactor analysis by forming the complete matrix over space moments and energy a robust set of solution strategies may be applied power iteration shifted power iteration rayleigh quotient iteration arnoldi s method and a generalized davidson method each using algebraic and physics based multigrid preconditioners have been compared on the c5g7 mox test problem as well as an operational pressurized water reactor model our results show that the most efficient approach is the generalized davidson method which is 30 40 times faster than traditional power iteration and 6 10 times faster than arnoldi s method

a novel multigrid method for sn discretizations of the mono energetic boltzmann transport equation in the optically thick and thin regimes with anisotropic scattering part i this paper presents a new multigrid method applied to the most common sn discretizations petrov galerkin diamond differenced corner balanced and discontinuous galerkin of the mono energetic boltzmann transport equation in the optically thick and thin regimes and with strong anisotropic scattering unlike methods that use scalar dsa diffusion preconditioners for the source iteration this multigrid method is applied directly to an integral equation for the scalar flux thus unlike the former methods that apply a multigrid strategy to the scalar dsa diffusion operator this method applies a multigrid strategy to the integral source iteration operator which is an operator for 5 independent variables in spatial three dimensions 3 d 3 in space and 2 in angle and 4 independent variables in spatial 2 d 2 in space and 2 in angle the core smoother of this multigrid method involves applications of the integral operator since the kernel of this integral operator involves the transport sweeps applyin

preconditioned hermitian and skew hermitian splitting methods for non hermitian positive semidefinite linear systems for the positive semidefinite system of linear equations of a block two by two structure by making use of the hermitian skew hermitian splitting iteration technique we establish a class of preconditioned hermitian skew hermitian splitting iteration methods theoretical analysis shows that the new method converges unconditionally to the unique solution of the linear system moreover the optimal choice of the involved iteration parameter and the corresponding asymptotic convergence rate are computed exactly numerical examples further confirm the correctness of the theory and the effectiveness of the method

bernstein sato polynomials for maximal minors and sub maximal pfaffians abstract we determine the bernstein sato polynomials for the ideal of maximal minors of a generic m n matrix as well as for that of sub maximal pfaffians of a generic skew symmetric matrix of odd size as a corollary we obtain that the strong monodromy conjecture holds in these two cases

arcs on determinantal varieties we study arc spaces and jet schemes of generic determinantal varieties using the natural group action we decompose the arc spaces into orbits and analyze their structure this allows us to compute the number of irreducible components of jet schemes log canonical thresholds and topological zeta functions

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

preconditioned hss methods for the solution of non hermitian positive definite linear systems and applications to the discrete convection diffusion equation we study the role of preconditioning strategies recently developed for coercive problems in connection with a two step iterative method based on the hermitian skew hermitian splitting hss of the coefficient matrix proposed by bai golub and ng for the solution of nonsymmetric linear systems whose real part is coercive as a model problem we consider finite differences fd matrix sequences an a p n discretizing the elliptic convection diffusion problem with being a plurirectangle of rd with a x being a uniformly positive function and p x denoting the reynolds function here for plurirectangle we mean a connected union of rectangles in d dimensions with edges parallel to the axes more precisely in connection with preconditioned hss gmres like methods we consider the preconditioning sequence pn a n pn a dn1 2 a an 1 0 dn1 2 a where dn a is the suitably scaled main diagonal of an a 0 if a x is positive and regular enough then the preconditioned sequence shows a strong clustering at unity so that the sequence pn a n turns out to be a superlinear preconditioning sequence for an a 0 n where an a 0 represents a good approximation of re an a p namely the real part of an a p the computational interest is due to the fact that the preconditioned hss method has a convergence behavior depending on the spectral properties of pn 1 a re an a p n pn 1 a an a 0 n therefore the solution of a linear system with coefficient matrix an a p is reduced to computations involving diagonals and to the use of fast poisson solvers for an 1 0 n some numerical experimentations confirm the optimality of the discussed proposal and its superiority with respect to existing techniques

on images of mori dream spaces the purpose of this paper is to study the geometry of images of morphisms from mori dream spaces first we prove that a variety which admits a surjective morphism from a mori dream space is again a mori dream space secondly we introduce a natural fan structure on the effective cone of mori dream spaces we show that it encodes the information of zariski decompositions which in turn is equivalent to the information of the variation of git quotients of their cox rings finally we show that under a surjective morphism between mori dream spaces the fan of the target space coincides with the restriction of the fan of the source

symmetry classes of alternating sign matrices under one roof in a previous article math co 9712207 we derived the alternating sign matrix asm theorem from the izergin korepin determinant for a partition function for square ice with domain wall boundary here we show that the same argument enumerates three other symmetry classes of alternating sign matrices vsasms vertically symmetric asms even htsasms half turn symmetric asms and even qtsasms quarter turn symmetric asms the vsasm enumeration was conjectured by mills the others by robbins math co 0008045 we introduce several new types of asms uasms asms with a u turn side uuasms two u turn sides osasms off diagonally symmetric asms oosasms off diagonally off antidiagonally symmetric and uosasms off diagonally symmetric with u turn sides uasms generalize vsasms while uuasms generalize vhsasms vertically and horizontally symmetric asms and another new class vhpasms vertically and horizontally perverse osasms oosasms and uosasms are related to the remaining symmetry classes of asms namely dsasms diagonally symmetric dasasms diagonally anti diagonally symmetric and tsasms totally symmetric asms we enumerate several of these new classes and we provide several 2 enumerations and 3 enumerations our main technical tool is a set of multi parameter determinant and pfaffian formulas generalizing the izergin korepin determinant for asms and the tsuchiya determinant for uasms solv int 9804010 we evaluate specializations of the determinants and pfaffians using the factor exhaustion method

multigrid in energy preconditioner for krylov solvers we have added a new multigrid in energy mge preconditioner to the denovo discrete ordinates radiation transport code this preconditioner takes advantage of a new multilevel parallel decomposition a multigroup krylov subspace iterative solver that is decomposed in energy as well as space angle forms the backbone of the transport solves in denovo the space angle energy decomposition facilitates scaling to hundreds of thousands of cores the multigrid in energy preconditioner scales well in the energy dimension and significantly reduces the number of krylov iterations required for convergence this preconditioner is well suited for use with advanced eigenvalue solvers such as rayleigh quotient iteration and arnoldi

on the birational geometry of spaces of complete forms ii skew forms abstract moduli spaces of complete skew forms are compactifications of spaces of skew symmetric linear maps of maximal rank on a fixed vector space where the added boundary divisor is simple normal crossing in this paper we compute their effective nef and movable cones the generators of their cox rings and for those spaces having picard rank two we give an explicit presentation of the cox ring furthermore we give a complete description of both the mori chamber and stable base locus decompositions of the effective cone of some spaces of complete skew forms having picard rank at most four

on inexact hermitian and skew hermitian splitting methods for non hermitian positive definite linear systems we study theoretical properties of two inexact hermitian skew hermitian splitting ihss iteration methods for the large sparse non hermitian positive definite system of linear equations in the inner iteration processes we employ the conjugate gradient cg method to solve the linear systems associated with the hermitian part and the lanczos or conjugate gradient for normal equations cgne method to solve the linear systems associated with the skew hermitian part respectively resulting in ihss cg lanczos and ihss cg cgne iteration methods correspondingly theoretical analyses show that both ihss cg lanczos and ihss cg cgne converge unconditionally to the exact solution of the non hermitian positive definite linear system moreover their contraction factors and asymptotic convergence rates are dominantly dependent on the spectrum of the hermitian part but are less dependent on the spectrum of the skew hermitian part and are independent of the eigenvectors of the matrices involved optimal choices of the inner iteration steps in the ihss cg lanczos and ihss cg cgne iterations are discussed in detail by considering both global convergence speed and overall computation workload and computational efficiencies of both inexact iterations are analyzed and compared deliberately

on the convergence of parallel chaotic nonlinear multisplitting newton type methods abstract a class of parallel chaotic nonlinear multisplitting newton type methods for solving the nonlinear system of equations f x 0 f d r n r n is established and its local convergence theory is presented

a fast algorithm to solve systems of nonlinear equations abstract a new hss based algorithm for solving systems of nonlinear equations is presented and its semilocal convergence is proved spectral properties of the new method are investigated performance profile for the new scheme is computed and compared with hss algorithm besides by a numerical example in which a two dimensional nonlinear convection diffusion equation is solved we compare the new method and the newton hss method numerical results show that the new scheme solves the problem faster than the newton hss scheme in terms of cpu time and number of iterations moreover the application of the new method is found to be fast reliable flexible accurate and has small cpu time

spatial multigrid for isotropic neutron transport a spatial multigrid algorithm for isotropic neutron transport is presented in x y geometry the linear system is obtained using discrete ordinates in angle and corner balance finite differencing in space spatial smoothing is accomplished by a four color block jacobi relaxation where the diagonal blocks correspond to 4 cell blocks on the spatial grid a bilinear interpolation operator and its transpose are used for the grid transfer operators good convergence factors were observed for homogeneous material properties heterogeneous material properties prove more difficult especially the case of a vacuum region surrounded by a thick diffusive region in this case a small amount of absorption or effective absorption in a time dependent problem restores good convergence numerical results are presented

on the conormal bundle of the determinantal variety call w such variety if we choose bases b v a a b u v i b for each module we can identify w with the variety of pairs of matrices y x with entries in r x being an m x n matrix y an ii x m matrix such that x y omx y x onxm now let a be the coordinate ring of the affine space a of dimension 2 m x n i e the polynomial ring r x yji i l m j i n and

on the biregular geometry of the fulton macpherson compactification abstract let x n be the fulton macpherson compactification of the configuration space of n ordered points on a smooth projective variety x we prove that if either n 2 or dim x 2 then the connected component of the identity of aut x n is isomorphic to the connected component of the identity of aut x when x c is a curve of genus g c 1 we classify the dominant morphisms c n c r and thanks to this we manage to compute the whole automorphism group of c n namely aut c n s n aut c for any n 2 while aut c 2 s 2 aut c aut c furthermore we extend these results on the automorphisms to the case where x c 1 c r is a product of curves of genus g c i 2 finally using the techniques developed to deal with fulton macpherson spaces we study the automorphism groups of some kontsevich moduli spaces m 0 n p n d

multigroup diffusion preconditioners for multiplying fixed source transport problems several preconditioners based on multigroup diffusion are developed for application to multiplying fixed source transport problems using the discrete ordinates method by starting from standard one group diffusion synthetic acceleration dsa a multigroup diffusion preconditioner is constructed that shares the same fine mesh as the transport problem as a cheaper but effective alternative a two grid coarse mesh multigroup diffusion preconditioner is examined for which a variety of homogenization schemes are studied to generate the coarse mesh operator finally a transport corrected diffusion preconditioner based on application of the newton shulz algorithm is developed the results of several numerical studies indicate the coarse mesh diffusion preconditioners work very well in particular a coarse mesh transport corrected diffusion preconditioner reduced the computational time of multigroup gmres by up to a factor of 17 and outperformed best case gauss seidel results by over an order of magnitude for all problems studied

advanced determinant calculus a complement abstract this is a complement to my previous article advanced determinant calculus c krattenthaler advanced determinant calculus seminaire lotharingien combin 42 1999 the andrews festschrift article b42q 67 pp in the present article i share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory g almkvist c krattenthaler j petersson some new formulas for experiment math 12 2003 441 456 moreover i add a list of determinant evaluations which i consider as interesting which have been found since the appearance of the previous article or which i failed to mention there including several conjectures and open problems

asymmetric hermitian and skew hermitian splitting methods for positive definite linear systems in this paper efficient iterative methods for the large sparse non hermitian positive definite systems of linear equations based on the hermitian and skew hermitian splitting of the coefficient matrix are studied these methods include an asymmetric hermitian skew hermitian ahss iteration and its inexact version the inexact asymmetric hermitian skew hermitian iahss iteration which employs some krylov subspace methods as its inner process we theoretically study the convergence properties of the ahss method and the iahss method moreover the contraction factor of the ahss iteration is derived numerical examples illustrating the effectiveness of both ahss and iahss iterations are presented

les degres des varietes des matrices nilpotentes abstract nous calculons les degres des adherences des orbites de matrices nilpotentes et en particulier ceux des varietes a rang et indice donnes