Showing papers in "International Journal of Computer Mathematics in 1994"
TL;DR: Some modifications are suggested to the controlled random search algorithm for global optimization that offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring ‘direct search’ type methods.
Abstract: Some modifications are suggested to the controlled random search algorithm for global optimization. Numerical experiments indicate that the resulting algorithms are considerably better than the originals and offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring ‘direct search’ type methods.
62 citations
TL;DR: In this paper, the problems related to finding a pattern common to all words in a given set are dealt with, where the authors restrict their attention to patterns expressible by the use of variables ranging over words.
Abstract: The paper deals with the problems related to finding a pattern common to all words in a given set We restrict our attention to patterns expressible by the use of variables ranging over words Two essentially different cases result, depending on whether or not the empty word belongs to the range We investigate equivalence and inclusion problems, patterns descriptive for a set, as well as some complexity issues The inclusion problem between two pattern languages turns out to be of fundamental theoretical importance because many problems in the classical combinatorics of words can be reduced to it
61 citations
TL;DR: This work extends the modified Gauss-Seidel method introduced by A. D. Gunawardena et al. and shows that this method is able to improve the rate of convergence compared to the modifiedGauss- Seidel method.
Abstract: We extend the modified Gauss-Seidel method introduced by A. D. Gunawardena et al. Some numerical examples show that our method is able to improve the rate of convergence compared to the modified Gauss-Seidel method.
52 citations
TL;DR: In this paper, the first and second kinds Chebyshev coefficients of the moments of the general order derivative of an infinitely differentiable function in terms of its Chebyshesv coefficients are given.
Abstract: Expressions for the first and second kinds Chebyshev coefficients of the moments of the general order derivative of an infinitely differentiable function in terms of its Chebyshev coefficients are given. Two numerical applications of how to use these expressions for solving ordinary differential equations with polynomial coefficients are described. Comparisons with the results obtained by Lewanowicz optimum algorithm (1976) are noted.
50 citations
TL;DR: This paper investigates the convergence of parallel multisplitting methods for solving linear systems Ax = b, where A is an H-matrix, and compares the asymptotic convergence rates of the parallel methods.
Abstract: This paper investigates the convergence of parallel multisplitting methods for solving linear systems Ax = b, where A is an H-matrix. Sufficient conditions of convergence for general parallel methods are derived. A class of parallel generalized AOR methods, parallel block AOR methods and parallel AOR methods are proposed, and many convergence conditions are obtained. In case A is an M-matrix, we compare the asymptotic convergence rates of the parallel methods.
36 citations
TL;DR: In this article, a class of odd-order obstacle boundary problems can be studied in the general framework of variational inequalities, which can be solved by using the quintic 5-splines.
Abstract: In this paper, we show that a class of odd order obstacle problems can be studied in the general framework of variational inequalities It is shown that the variational inequalities can be formulated as a system of variational equations without constraint, which can be solved by using the quintic 5-splines We describe numerical experience on the use of penalty function method for obtaining numerical solution of a class of odd order obstacle boundary problems arising in the physical oceanography
32 citations
TL;DR: This paper introduces genetic algorithms for the level permutation problem (LPP) and shows that genetic algorithms outperform the previously known heuristics especially when applied to low density graphs.
Abstract: This paper introduces genetic algorithms for the level permutation problem (LPP). The problem is to minimize the number of edge crossings in a bipartite graph when the order of vertices in one of the two vertex subsets is fixed. We show that genetic algorithms outperform the previously known heuristics especially when applied to low density graphs. Values for various parameters of genetic LPP algorithms are tested.
30 citations
TL;DR: This paper investigates the classical regulated rewriting mechanisms like programmed grammars, matrix Grammars and ordered grammARS considered as accepting devices, in contrast with the usual generating mode, and obtains that ordered gramMars with context-free rules, admitting γ-productions, are computationally universal in accepting mode.
Abstract: In this paper, we investigate the classical regulated rewriting mechanisms like programmed grammars, matrix grammars and ordered grammars considered as accepting devices, in contrast with the usual generating mode. Where in the type-n grammars of the Chomsky hierarchy the descriptive power both of generating and of accepting grammars coincide, this need not be true any more in regulated devices. We even obtain, e.g., that ordered grammars with context-free rules and γ-free productions accept all context- sensitive γ-free languages, and that ordered grammars with context-free rules, admitting γ-productions, are computationally universal in accepting mode.
27 citations
TL;DR: In this paper, a special class of Hopscotch Algorithms for the finite difference solution of the diffusion equation is considered, which is very efficient with regard to parallel computing in MIMD and ease of programming.
Abstract: In this paper, a special class of Hopscotch Algorithms for the finite difference solution of the diffusion equation is considered. The algorithm is very efficient with regard to parallel computing in MIMD and ease of programming. A better convergence of the difference solution is proved without the conditions of either Δt/Δx 2 = C or Δt/Δx→0 as Δt→ 0 and Δx→0. Numerical examples of the method are included.
25 citations
TL;DR: Several modified third order Runge-Kutta formulas based on a variety of means are developed, but the arithmetic mean (AM) formula which shortens the process of calculations does not yield the highest degree of accuracy.
Abstract: Several modified third order Runge-Kutta formulas based on a variety of means are developed. The arithmetic mean (AM) formula which shortens the process of calculations does not yield the highest degree of accuracy obtained by using some of the new formulas. The accuracy of the new formulas are numerically tested and compared.
24 citations
TL;DR: In this paper, it was shown that a two-parameter family of methods which are one-step, fourth-order and A-stable can be obtained, and that there exists a sub-family of these methods that are, in addition, L-stable.
Abstract: Recently, Kondrat and Jacques [1] gave an extended two-step fourth order A-stable method; the reason noted for giving a two-step method is that a one-step method of the type is not possible. Firstly, we show that it is possible to obtain a two-parameter family of such methods which are one-step, fourth order and A-stable; and, there exists a one-parameter sub-family of these methods which are, in addition, L-stable. Secondly, from among the extended two-step methods, it is natural to ask if the well-known Simpson's rule can be stabilized; we present an A-stabilized version of Simpson's rule.
TL;DR: In this paper, a fourth order Runge-Kutta method based on the harmonic mean (HM) averaging of the functional values is presented. But the accuracy of the new formula is numerically examined.
Abstract: The new Runge-Kutta formulation using some other means other than the conventional arithmetic mean has resulted in the introduction of a number of new formulae for the numerical solution of ODE's. This paper discusses the derivation of a fourth order Runge-Kutta method based on the harmonic mean (HM) averaging of the functional values. The accuracy of the new formula is numerically examined.
TL;DR: In this article, an alternative method based on substitution is presented, and this method is compared with other approaches, and tests are carried out on a representative set of examples, and the algorithms are applied to problems with large oscillatory factors.
Abstract: Many current problems in applied mathematics require the numerical integration of irregular oscillatory integrals. Few methods have been specifically found for these problems. An alternative method based on substitution is presented here and this method is compared with other approaches. Tests are carried out on a representative set of examples, and the algorithms are applied to problems with large oscillatory factors.
TL;DR: Some variants of deletion operations which generalize the left/right quotient of languages are studied, and how these deletions can be expressed as a combination of other operations, and on closure properties of various language families under deletion are studied.
Abstract: The paper studies some variants of deletion operations which generalize the left/right quotient of languages. The main emphasis is put on how these deletions can be expressed as a combination of other operations, and on closure properties of various language families under deletion. Some results are the expected ones: the sequential (iterated sequential, dipolar) deletion from a regular language produces a regular set regardless of the complexity of the deleted language. On the other hand, it still remains a challenging open problem whether or not the family of regular languages is closed under iterated parallel deletion with singletons
TL;DR: It is shown, that for banded symmetric positive definite (SPD) circulant matrices with bandwidth p and elements satisfying an efficient tridiagonalcirculant preconditioner can be designed.
Abstract: A tridiagonal circulant preconditioner for banded symmetric circulant linear systems which occur in digital signal processing (DSP) problems is studied. It is shown, that for banded symmetric positive definite (SPD) circulant matrices with bandwidth p and elements satisfying an efficient tridiagonal circulant preconditioner can be designed. The influence of a preconditioning parameter w on the condition number of the preconditioned linear system is studied and a formula for estimating is proposed.
TL;DR: It is shown that under some conditions the preconditioned S OR method gives improvement in the rate of convergence compared with the unpreconditioned SOR method for 0 1.
Abstract: In this paper we investigate how the convergence rate of the successive overrelaxation (SOR) method is affected if the linear system Ax = b is preconditioned by performing certain elementary row operations on A. It is shown that under some conditions the preconditioned SOR method gives improvement in the rate of convergence compared with the unpreconditioned SOR method for 0 1.
TL;DR: In this article, the authors presented the block Accelerated Overrelaxation iterative method (AOR) to approximate the solution of the matrix equation AX - XB - C. An analytic determination of good values of the involved real parameters of this iteration method is presented in terms of certain bounds on the eigenvalues of the iteration matrix.
Abstract: In this paper we present the block Accelerated Overrelaxation iterative method (AOR) to approximate the solution of the matrix equation AX - XB - C. An analytic determination of good values of the involved real parameters of this iterative method is presented in terms of certain bounds on the eigenvalues of the iteration matrix.
TL;DR: In this article, the authors extended earlier work on the solution of the constant-coefficient two-dimensional diffusion equation by considering two classes of time-split finite-difference methods, namely locally one-dimensional (LOD) schemes and alternating direction implicit (ADI) methods.
Abstract: This paper extends earlier work on the solution of the constant-coefficient two-dimensional diffusion equation by considering two classes of time-split finite-difference methods, namely locally one-dimensional (LOD) schemes and alternating direction implicit (ADI) methods. Two new fourth-order techniques are described and tested. Firstly, a LOD method based on the fourth-order explicit Noye-Hayman procedure for the one-dimensional diffusion equation is described. Proper treatment of values at, and adjacent to, the boundary at intermediate time levels is necessary, otherwise the method degenerates to second-order. Secondly, an unconditionally stable ADI method based on a (3,9) two-dimensional computational molecule is developed and tested.
TL;DR: In this paper, an index of the convexity measure by means of the logarithmic operator is defined, and a family of Newton type iterative processes to solve a complex or scalar nonlinear equation is defined.
Abstract: In this paper, we define an index of the convexity measure by means of the logarithmic operator. As an application, we study the influence of the convexity on Newton method for solving nonlinear equations. Then we define a family of Newton type iterative processes to solve a complex or scalar nonlinear equation, we can always apply an iterative process of this family faster than Newton method.
TL;DR: An algorithm that dynamically constructs DAWGs (Directed Acyclic Word Graphs) for the handling of dynamic key sets and solves the problem of the increasing number of transitions in the trie structure is proposed.
Abstract: SCOPE: Algorithms, Information storage and retrieval. A trie is a search tree obtained by merging the common suffixes of the key set. It has the advantage that all keys as prefixes of an input string can be retrieved with high speed. When the size of the key set is enlarged, however, a problem arises, as the number of transitions increases, so too does the need for a large storage capacity. This paper proposes an algorithm that dynamically constructs DAWGs (Directed Acyclic Word Graphs) for the handling of dynamic key sets. It also solves the problem of the increasing number of transitions in the trie structure. The proposed method constructs a DAWG through the local separation of common suffixes for updating a key and, after finishing updating a key, the local transition merge of common suffixes. The proposed algorithm is theoretically evaluated and the data structure for the implementation is discussed. Experimental results show that the number of transitions in the DAWG is reduced by approx. 50 to 70% ...
TL;DR: In this paper, the spectral radii of the matarices M -1 N and L γω which is the AOR type matrix were discussed and new results for the convergence domains of the GAOR and GAOR, SOR and GSOR iterative methods with strictly or irreducibly diagonally dominant matrices were obtained.
Abstract: Using a concise method, different from those in [1-3, 7, 8] used by K. R. James, M. Martins and Hu Jia-gan, repectively, this paper discusses the upper bounds of the spectral radii of the matarices M -1 N and L γω which is the AOR type matrix, and gives new results. Based on these conclusions further results for the convergence domains of the AOR and GAOR, SOR and GSOR iterative methods with strictly or irreducibly diagonally dominant matrices are obtained. Finally conditions equivalent to the statement that the matrix is strictly or irreducibly diagonally dominant by rows are established.
TL;DR: Kim and Sukhatme as mentioned in this paper derived new mathematical series results for non-relativistic perturbation theory, which were then used to obtain a mathematical series result for the alternative approach.
Abstract: New perturbation theory expressions obtained by Kim and Sukhatme [“Alternative approach to non-relativistic perturbation theory”, J. Phys. A 25 (1992) L647–L650] are equated to standard perturbation theory expressions in order to obtain new mathematical series results. Several such new results are derived and discussed.
TL;DR: This paper counts, list and generate randomly hybrid binary trees using Fibonacci numbers, and considers binary trees whose internal nodes are either associative or non-associative.
Abstract: We consider in this paper binary trees whose internal nodes are either associative or non-associative. Hybrid binary trees are equivalence classes with respect to the associative property. We count, list and generate randomly hybrid binary trees using Fibonacci numbers.
TL;DR: The present paper generalizes the method from [1] by using the Choleski factors of a term from a special splitting of the Gramian like a particular case, and observes that such a kind of splitting can be obtained by an incomplete Cholesky decomposition of the gramian.
Abstract: In the paper [1] the author proves that preconditioning the discrete Galerkin system by the Choleski factors of the Gramian we obtain a mesh independent condition number. In the present paper we generalize this method by using the Choleski factors of a term from a special splitting of the Gramian. Thus, we obtain the method from [1] like a particular case. We also observe that such a kind of splitting can be obtained by an incomplete Choleski decomposition of the Gramian.
TL;DR: Several algorithms of relaxed parallel chaotic iterative methods for solving large nonsingular systems of equations Ax = b are given and corresponding sufficient conditions of convergence for some relaxed parameters are obtained.
Abstract: In this paper we relax the some given models of parallel chaotic iterations and give several algorithms of relaxed parallel chaotic iterative methods for solving large nonsingular systems of equations Ax = b. Under some different assumptions of coefficient matrix A and its multisplittings we obtain corresponding sufficient conditions of convergence for some relaxed parameters.
TL;DR: In this article, the Alternating Group Explicit (AGE) algorithm is reformulated to solve a general coupled system of elliptic partial differential equations, which has proved to offer many advantages in its use as an explicit scheme in various applications.
Abstract: In this paper, the Alternating Group Explicit (AGE) algorithm, which has proved to offer many advantages in its use as an explicit scheme in various applications, is now reformulated to solve a general coupled system of elliptic partial differential equations. Computational results are obtained to demonstrate the applicability of the method on some specific problems, i.e. the Biharmonic and Navier-Stokes equations.
TL;DR: Some properties of the shortest vectorial addition chain are presented and an approach to achieve the shortest chains in some special cases is proposed.
Abstract: The concept of the shortest vectorial addition chains is considered to be an optimal approach for computing a monomial inimum number of multiplications In this paper, some properties of the shortest vectorial addition chain are presented Furthermore, an approach to achieve the shortest chains in some special cases is proposed The correctness of these properties and the optimality of this approach are also shown
TL;DR: In this paper, it was shown that when Newton-like methods are applied to operator equations in Banach space as well as to finite-dimensional discretizations of these equations, there is at most a difference of one between the number of steps required by the two iterations to converge within a given tolerance.
Abstract: In this paper we show that when Newton-like methods are applied to operator equations in Banach space as well as to finite-dimensional discretizations of these equations then there is at most a difference of one between the number of steps required by the two iterations to converge within a given tolerance.
TL;DR: In this paper, a class of stable nonlinear trapezoidal formulas based on a variety of means for solving initial value problems of the form is developed, and the accuracy and stability of the new formulas are investigated.
Abstract: A class of stable nonlinear trapezoidal formulas based on a variety of means for solving initial value problems of the form is developed. The accuracy and stability of the new formulas are investigated. Numerical tests are carried out to compare the results of the established methods with the results of the existing formulas.
TL;DR: In this paper, a sequence of modified quasi-interpolatory splines is introduced for numerical evaluation of Cauchy principal value integrals, and uniform convergence is proved for a series of locally uniform partitions of the integration interval.
Abstract: A sequence of modified quasi-interpolatory splines is introduced for numerical evaluation of Cauchy principal value integrals. Uniform convergence is proved, for a sequence of locally uniform partitions of the integration interval.