experimental study of ilu preconditioners for indefinite matrices incomplete lu factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indefinite matrices however their failure rate is still too high for them to be useful as black box library software for general matrices besides fatal breakdowns due to zero pivots the major causes of failure are inaccuracy and instability of the triangular solves when there are small pivots both these problems can occur but these problems can also occur without small pivots through examples from actual problems this paper shows how these problems evince themselves how these problems can be detected and how these problems can sometimes be circumvented through pivoting reordering scaling perturbing diagonal elements and preserving symmetric structure the goal of this paper is to gain a better practical understanding of ilu preconditioners and help improve their reliability

some isometric embedding and rigidity results for riemannian manifolds in this note we announce some new results concerning rigidity and isometric embeddings of riemannian manifolds a special case of the main result states that a general mn unk rn r r n 1 n 2 2 is uniquely determined up to finitely many constants by its induced ds2

bilum block versions of multielimination and multilevel ilu preconditioner for general sparse linear systems we introduce block versions of the multielimination incomplete lu ilum factorization preconditioning technique for solving general sparse unstructured linear systems these preconditioners have a multilevel structure and for certain types of problems may exhibit properties that are typically enjoyed by multigrid methods several heuristic strategies for forming blocks of independent sets are introduced and their relative merits are discussed the advantages of block ilum over point ilum include increased robustness and efficiency we compare several versions of the block ilum point ilum and the dual threshold based ilut preconditioners in particular tests with some convection diffusion problems show that it may be possible to obtain convergence that is nearly independent of the reynolds number as well as of the grid size

the linearized system for isometric embeddings and its characteristic variety abstract in this paper we prove a conjecture of bryant griffiths and yang concerning the characteristic variety for the determined isometric embedding system in particular we show that the characteristic variety is not smooth for any dimension greater than 4 this is accomplished by introducing a smaller yet equivalent linearized system in an appropriate way which facilitates analysis of the characteristic variety

on the constructions of constant weight codes two methods of constructing binary constant weight codes from 1 codes over gf q and 2 constant weight codes over gf q are presented several classes of binary optimum constant weight codes are derived from these methods in general we show that binary optimum constant weight codes which achieve the johnson bound can be constructed from optimum codes over gf q which achieve the plotkin bound finally several classes of optimum constant weight codes over gf q are constructed

linear size optimal q ary constant weight codes and constant composition codes an optimal constant composition or constant weight code of weight w has linear size if and only if its distance d is at least 2w 1 when d 2w the determination of the exact size of such a constant composition or constant weight code is trivial but the case of d 2w 1 has been solved previously only for binary and ternary constant composition and constant weight codes and for some sporadic instances this paper provides a construction for quasicyclic optimal constant composition and constant weight codes of weight w and distance 2w 1 based on a new generalization of difference triangle sets as a result the sizes of optimal constant composition codes and optimal constant weight codes of weight w and distance 2w 1 are determined for all such codes of sufficiently large lengths this solves an open problem of etzion the sizes of optimal constant composition codes of weight w and distance 2w 1 are also determined for all w 6 except in two cases

constructions for q ary constant weight codes this paper introduces a new combinatorial construction for q ary constant weight codes which yields several families of optimal codes and asymptotically optimal codes the construction reveals intimate connection between q ary constant weight codes and sets of pairwise disjoint combinatorial designs of various types

bounds and constructions for ternary constant composition codes the problem of determining the maximum size of a ternary code is considered under the restriction that each symbol should appear a given number of times in each codeword upper and lower bounds on the size of such codes under the hamming metric are discussed where the lower bounds follow from constructions of good codes some of the results are obtained by explicitly finding codes by computer search a table of exact values and best known bounds on the maximum size for codes of length at most 10 is presented

preconditioned krylov subspace methods for solving nonsymmetric matrices from cfd applications abstract we conduct an experimental study on the behavior of several preconditioned iterative methods to solve nonsymmetric matrices arising from computational fluid dynamics cfd applications the preconditioned iterative methods consist of krylov subspace accelerators and a powerful general purpose multilevel block ilu bilum preconditioner the bilum preconditioner and an enhanced version of it are slightly modified versions of the originally proposed preconditioners they will be used in combination with different krylov subspace methods we choose to test three popular transpose free krylov subspace methods bicgstab gmres and tfqmr numerical experiments using several sets of test matrices arising from various relevant cfd applications are reported

optimal ternary constant weight codes of weight four and distance six recently chee and ling constructions for q ary constant weight codes ieee trans inf theory vol 53 no 1 135 146 jan 2007 introduced a new combinatorial construction for q ary constant weight codes which reveals a close connection between q ary constant weight codes and sets of pairwise disjoint combinatorial designs in this paper we study the problem of constructing optimal ternary constant weight codes with hamming weight four and minimum distance six using this approach the construction here exploits completely reducible super simple designs and group divisible codes the problem is solved leaving only two cases undetermined previously the sizes of constant weight codes of weight four and distance six were known only for those of length no greater than 10

enhanced multi level block ilu preconditioning strategies for general sparse linear systems abstract this paper introduces several strategies to deal with pivot blocks in multi level block incomplete lu factorization bilum preconditioning techniques these techniques are aimed at increasing the robustness and controlling the amount of fill ins of bilum for solving large sparse linear systems when large size blocks are used to form block independent set techniques proposed in this paper include double dropping strategies approximate singular value decomposition variable size blocks and use of an arrowhead block submatrix we point out the advantages and disadvantages of these strategies and discuss their efficient implementations numerical experiments are conducted to show the usefulness of the new techniques in dealing with hard to solve problems arising from computational fluid dynamics in addition we discuss the relation between multi level ilu preconditioning methods and algebraic multi level methods

a preconditioned krylov technique for global hydrodynamic stability analysis of large scale compressible flows the combination of iterative krylov based eigenvalue algorithms and direct numerical simulations dns has proven itself an effective and robust tool in solving complex global stability problems of compressible flows a cayley transformation is required to add flexibility to our stability solver and to allow access to specific parts of the full global spectrum which would be out of reach without such a transformation in order to robustify the overall global stability solver an efficient ilu based preconditioner has been implemented with this cayley transformed dns based krylov method two flow cases were successfully investigated i a compressible mixing layer a rather simple but well known problem which served as a test case and ii a supersonic flow about a swept parabolic body a challenging large scale flow configuration

optimal ternary constant composition codes of weight four and distance five constant composition codes cccs are a generalization of constant weight codes and permutation codes the concept of group divisible codes an analog of group divisible designs in combinatorial design theory was first introduced by chee et al this new class of codes has been shown to be useful in recursive constructions of constant weight codes and constant composition codes in this paper we consider the problem of determining the maximal sizes of ternary constant composition codes of weight four and distance five using group divisible codes as the main tools we determine the exact values for these parameters the previously known results are those with code length no greater than 10

the sizes of optimal q ary codes of weight three and distance four a complete solution this correspondence introduces two new constructive techniques to complete the determination of the sizes of optimal q ary codes of constant weight three and distance four

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

cyclic constant weight codes upper bounds and new optimal constructions in this paper we consider optimal q ary cyclic constant weight codes of length n minimum distance d and weight w briefly cyclic n d w q codes we introduce the pure and mixed difference method to present a combinatorial description for a cyclic n d w q code and then obtain some tight upper bounds on the sizes of optimal cyclic n d w q codes finally by using skolem type sequences we completely determine the sizes of optimal cyclic n d 3 3 codes with minimum distance 1 leq d leq 6

optimal quaternary constant weight codes with weight four and distance five constant weight codes play an important role in coding theory the problem of determining the sizes for optimal quaternary constant weight codes with length n weight 4 and minimum hamming distance 5 n 5 4 4 codes has been investigated in several papers although some constructions and several infinite families for such codes with length n 0 1 mod 4 have been given the problem is still far from complete in this paper we determine the size of an optimal n 5 4 4 code for each integer n 4 leaving 55 lengths unsolved especially for length n 0 1 mod 4 the existence problem of the equivalent combinatorial object namely the generalized steiner system is solved leaving only seven values undetermined

incomplete lu preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems we consider the preconditioned iterative solution of large dense linear systems where the coefficient matrix is a complex valued matrix arising from discretizing the integral equation of electromagnetic scattering for some scattering structures this matrix can be poorly conditioned the main purpose of this study is to evaluate the efficiency of a class of incomplete lu ilu factorization preconditioners for solving this type of matrices we solve the electromagnetic wave equations using the bicg method with an ilu preconditioner in the context of a multilevel fast multipole algorithm mlfma the novelty of this work is that the ilu preconditioner as constructed using the near part block diagonal submatrices generated from the mlfma experimental results show that the ilu preconditioner reduces the number of bicg iterations substantially compared to the block diagonal preconditioner the preconditioned iteration scheme also maintains the computational complexity of the mlfma and consequently reduces the total cpu time

group divisible codes and their application in the construction of optimal constant composition codes of weight three the concept of group divisible codes a generalization of group divisible designs with constant block size is introduced in this paper this new class of codes is shown to be useful in recursive constructions for constant weight and constant composition codes large classes of group divisible codes are constructed which enabled the determination of the sizes of optimal constant composition codes of weight three and specified distance leaving only four cases undetermined previously the sizes of constant composition codes of weight three were known only for those of sufficiently large length

sparse approximate inverse preconditioners using norm minimization techniques we investigate the use of sparse approximate inverse preconditioners for the iterative solution of unsymmetric linear systems of equations we consider the approximations proposed by cosgrove diaz and griewank internat j comput math 44 1992 pp 91 110 and huckle and grote a new approach to parallel preconditioning with sparse approximate inverses tech report sccm 94 03 stanford university 1994 which are based on norm minimization techniques such methods are of particular interest because of the considerable scope for parallelization we propose a number of enhancements which may improve their performance when run in a sequential environment these methods can perform unfavorably when compared with other techniques however they can be successful when other methods fail and simulations indicate that they can be competitive when considered in a parallel environment

on constant composition codes over z sub q a constant composition code is a special constant weight code under the restriction that each symbol should appear a given number of times in each codeword in this correspondence we give a lower bound for the maximum size of the q ary constant composition codes with minimum distance at least 3 this bound is asymptotically optimal and generalizes the graham sloane bound for binary constant weight codes in addition three construction methods of constant composition codes are presented and a number of optimum constant composition codes are obtained by using these constructions

a sparse approximate inverse preconditioner for nonsymmetric linear systems this paper is concerned with a new approach to preconditioning for large sparse linear systems a procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient type methods some theoretical properties of the preconditioner are discussed and numerical experiments on test matrices from the harwell boeing collection and from tim davis s collection are presented our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners furthermore the new technique insures convergence rates of the preconditioned iteration which are comparable with those obtained with standard implicit preconditioners

characteristics and existence of isometric embeddings soit m ds 2 une variete de riemann c a 3 dimensions et x 0 m un point tel que le tenseur d einstein 7b g x 0 n est pas l 2 ou l t x0 m alors il existe un plongement isometrique local c d un voisinage de x 0 dans e 6

approximate inverse techniques for block partitioned matrices this paper proposes some preconditioning options when the system matrix is in block partitioned form this form may arise naturally for example from the incompressible navier stokes equations or may be imposed after a domain decomposition reordering approximate inverse techniques are used to generate sparse approximate solutions whenever these are needed in forming the preconditioner the storage requirements for these preconditioners may be much less than for incomplete lu factorization ilu preconditioners for tough large scale computational fluid dynamics cfd problems the numerical experiments show that these preconditioners can help solve difficult linear systems whose coefficient matrices are highly indefinite

a sparse approximate inverse preconditioner for parallel preconditioning of general sparse matrices a factored sparse approximate inverse is computed and used as a preconditioner for solving general sparse matrices the algorithm is derived from a matrix decomposition algorithm for inverting dense nonsymmetric matrices several strategies and special data structures are proposed to implement the algorithm efficiently sparsity patterns of the factored inverse are exploited to reduce computational cost the preconditioner possesses greater inherent parallelism than traditional preconditioners based on incomplete lu factorizations numerical experiments are used to show the effectiveness and efficiency of the proposed sparse approximate inverse preconditioner

a grid based multilevel incomplete lu factorization preconditioning technique for general sparse matrices we design a grid based multilevel incomplete lu preconditioner gilum for solving general sparse matrices this preconditioner combines a high accuracy ilu factorization with an algebraic multilevel recursive reduction the gilum preconditioner is a compliment to the domain based multilevel block ilut preconditioner a major difference between these two preconditioners is the way that the coarse level nodes are chosen the approach of gilum is analogous to that of algebraic multigrid method the gilum approach avoids some controversial issues in algebraic multigrid method such as how to construct the interlevel transfer operators and how to compute the coarse level operator numerical experiments are conducted to compare gilum with other ilu preconditioners

optimal ternary constant weight codes with weight 4 and distance 5 constant weight codes cwcs play an important role in coding theory the problem of determining the sizes for optimal ternary cwcs with length n weight 4 and minimum hamming distance 5 n 5 4 3 code has been settled for all positive integers n 10 or n 10 and n 1 mod 3 with n 13 52 58 undetermined in this paper we investigate the problem of constructing optimal n 5 4 3 codes for all lengths n with the tool of group divisible codes we determine the size of an optimal n 5 4 3 code for each integer n 4 leaving the lengths n 12 13 21 27 33 39 45 52 unsolved

a priori bounds for co dimension one isometric embeddings let x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i be a c 4 isometric embedding of a c4 metric g of nonnegative sectional curvature on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i into the euclidean space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i we prove a priori bounds for the trace of the second fundamental form h in terms of the scalar curvature r of g and the diameter d of the space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i g these estimates give a bound on the extrinsic geometry in terms of intrinsic quantities they generalize estimates originally obtained by weyl for the case n 2 and positive curvature and then by p guan and the first author for nonnegative curvature and n 2 using c 2 interior estimates of evans and krylov for concave fully nonlinear elliptic partial differential equations these bounds allow us to obtain the following convergence theorem for any 0 the set of metrics of nonnegative sectional curvature and scalar curvature bounded below by which are isometrically embedable in euclidean space inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 06i is closed in the holder space c 4 0 suppose that g is a smooth metric of nonnegative sectional curvature and positive scalar curvature on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 07i which admits locally convex isometric embedding into inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 08i does inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 09i g then admit a smooth global isometric embedding x inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 10i g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 11i

a transpose free quasi minimal residual algorithm for non hermitian linear systems the biconjugate gradient method bcg for solving general non hermitian linear systems ax b and its transpose free variant the conjugate gradients squared algorithm cgs both typically exhib

a lower bound for ternary constant weight codes we derive a lower bound for ternary constant weight codes with minimum hamming distance three the bound is similar to a bound for binary constant weight codes with minimum distance four described by graham and sloane 1980 it improves upon the gilbert 1952 bound and coincides asymptotically with the johnson 1962 bound for fixed weight as the codeword length tends to infinity

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

isometric immersions of surfaces with two classes of metrics and negative gauss curvature the isometric immersion of two dimensional riemannian manifolds or surfaces with negative gauss curvature into the three dimensional euclidean space is studied in this paper the global weak solutions to the gauss codazzi equations with large data in l infty are obtained through the vanishing viscosity method and the compensated compactness framework the l infty uniform estimate and h 1 compactness are established through a transformation of state variables and construction of proper invariant regions for two types of given metrics including the catenoid type and the helicoid type the global weak solutions in l infty to the gauss codazzi equations yield the c1 1 isometric immersions of surfaces with the given metrics

a lower bound for a n 4 w corresp an explicit lower bound is given for a n 4 w the maximum number of codewords in a binary code of length n minimum distance four and constant weight w