Showing papers in "International Journal of Computer Mathematics in 2001"
TL;DR: Experimental results on the major benchmarking functions used for performance evaluation of Genetic Algorithms (GAs) are presented, including the effect of population size, crossover probability, mutation rate and pseudorandom generator.
Abstract: This paper presents experimental results on the major benchmarking functions used for performance evaluation of Genetic Algorithms (GAs). Parameters considered include the effect of population size, crossover probability, mutation rate and pseudorandom generator. The general computational behavior of two basic GAs models, the Generational Replacement Model (GRM) and the Steady State Replacement Model (SSRM) is evaluated.
340 citations
TL;DR: A class of four-step methods each with three functions evaluation per iteration each based on collocation of the differential system at selected grid points which ensures the symmetry of the methods.
Abstract: An important factor among others that should be considered in developing a numerical integrator for the solution of ordinary differential equations is the prudent management of computer time, which depends essentially on the number of functions to be evaluated per iteration. Recognising the importance of this factor, this article therefore proposes a class of four-step methods each with three functions evaluation per iteration. The procedure which yields a system of equations for stepnumber k ≥ 4 is based on collocation of the differential system at selected grid points which ensures the symmetry of the methods. The methods are compared for accuracy and computer time with an existing four-step method containing five functions evaluation per iteration (see Awoyemi, 1999a). Three other Predictors are similarly proposed for use in the main method.
79 citations
TL;DR: A Collocation method is presented here for the Regularized Long Wave (RLW) equation by using Quadratic B-splines at mid points as element shape functions and it is proved that the number of solitons which are generated from Maxwellian initial conditions are determined.
Abstract: A Collocation method is presented here for the Regularized Long Wave (RLW) equation by using Quadratic B-splines at mid points as element shape functions. A linear stability analysis shows the scheme to be unconditionally stable. Test problems, including the migration and interaction of solitary waves, are used to validate the method which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied, and then we prove that the number of solitons which are generated from Maxwellian initial conditions are determined and we compare our results with earlier studies.
65 citations
TL;DR: An efficient and numerically stable algorithm for computing the positive definite solution of the nonlinear equation and some properties of the solution are discussed as well as the sufficient conditions for the existence are obtained.
Abstract: In this paper, an efficient and numerically stable algorithm for computing the positive definite solution of the nonlinear equation is proposed. Some properties of the solution are discussed as well as the sufficient conditions for the existence are obtained. Numerical examples are given to illustrate the accuracy of the proposed technique, which depend on iterative process
60 citations
TL;DR: This paper compares sequential string matching algorithms based on different approaches including classical, suffix automata, bit-parallelism and hashing in terms of the number of character comparisons and the running time for four different types of text.
Abstract: In this paper we present a short survey and experimental results for well known sequential string matching algorithms. We consider algorithms based on different approaches including classical, suffix automata, bit-parallelism and hashing. We put special emphasis on algorithms recently presented such as Shift-Or and BNDM algorithms. We compare these algorithms in terms of the number of character comparisons and the running time for four different types of text: binary alphabet, alphabet of size 8, English alphabet and DNA alphabet.
57 citations
TL;DR: This paper presents a technique for constructing state diagrams to facilitate mappings and is a specialization of an incomplete generic process described by Bially.
Abstract: The Hilbert Curve describes a method of mapping between one and n dimensions. Such mappings are of interest in a number of application domains including image processing and, more recently, in the indexing of multi-dimensional data. Relatively little work, however, has been devoted to techniques for mapping in more that 2 dimensions. This paper presents a technique for constructing state diagrams to facilitate mappings and is a specialization of an incomplete generic process described by Bially. Although the storage requirements for state diagrams increase exponentially with the number of dimensions, they are useful in up to about 9 dimensions.
42 citations
TL;DR: The (T,S) splitting method of A = U- V such that R(U)=AT and for computing the generalized inverse is established and the characteristics of the solution are developed.
Abstract: Given a real rectangular matrix A. In this paper the (T,S) splitting method of A = U- V such that R(U)=AT and for computing the generalized inverse is established. In consideration of the rectangular systems Au =f, we show that the sequence of the iterations converges to if and only if the spectral radius of is less than unity. The characteristics of the solution are developed. We present convergent conditions of the iteration matrix , and generalize the results of Coliatz and Marek and Szyld on monotone type iterations. Some criteria under regularity assumptions for comparing convergence rates of are given, where are (T,S) splittings of A
39 citations
TL;DR: A new method for obtaining a compact subsumptive general solution of a system of Boolean equations is presented, which relies on the use of the variable-entered Karnaugh map (VEKM) to achieve successive elimination through successive map folding.
Abstract: A new method for obtaining a compact subsumptive general solution of a system of Boolean equations is presented. The method relies on the use of the variable-entered Karnaugh map (VEKM) to achieve successive elimination through successive map folding. It is superior in efficiency and simplicity to methods employing Marquand diagrams or Conventional Karnaugh maps; it requires the construction of significantly smaller maps and produces such maps in a minimization-ready form. Moreover, the method is applicable to general Boolean equations and is not restricted to the two-valued case. Details of the method are carefully explained and then illustrated via a classical example.
38 citations
TL;DR: A numerical method for computing approximations for the solutions of a system of third order boundary value problems associated with odd order obstacle problems in physical oceanography is developed and shows that it gives numerical results which are better than the other available results.
Abstract: We develop a numerical method for computing approximations for the solutions of a system of third order boundary value problems associated with odd order obstacle problems. Such a problem arise in physical oceanography and can be studied in the framework of variational inequality theory. We study the convergence analysis of the present method and we show that it gives numerical results which are better than the other available results. Numerical example is presented to illustrate the applicability of the new method.
35 citations
TL;DR: The present sequel to these earlier works is to consider a family of such integrals of the products of Laguerre, Hermite, and other classical orthogonal polynomials in a systematic and unified manner.
Abstract: The evaluation of an integral of the product of Laguerre polynomials was discussed recently in this Journal by Mavromatis [12] (1990) and Lee [9] (1997) [see also Ong and Lee [14] (2000)]. The main object of the present sequel to these earlier works is to consider a family of such integrals of the products of Laguerre, Hermite, and other classical orthogonal polynomials in a systematic and unified manner. Relevant connections of some of these integral formulas with various known integrals, as well as the computational and numerical aspects of the results presented here, are also pointed out.
34 citations
TL;DR: It is proved that the recursively enumerable languages can be generated by systems with arbitrarily many membranes and bounded energy; when bounding the number of membranes and leaving free the quantity of energy associated with each rule, this feature is rather powerful.
Abstract: We consider P systems where each evolution rule “Produces” or “Consumes” some quantity of energy, in amounts which are expressed as integer numbers. In each moment and in each membrane the total energy involved in an evolution step should be positive, but if “Soo much” energy is present in a membrane, then the membrane will be destroyed (dissolved). We show that this feature is rather powerful. In the case of multisets of symbol-objects we find that systems with two membranes and arbitrary energy associated with rules, or with arbitrarily many membranes and a bounded energy associated with rules characterize the recursively enumerable sets of vectors of natural numbers (catalysts and priorities are used). In the case of string-objects we have only proved that the recursively enumerable languages can be generated by systems with arbitrarily many membranes and bounded energy; when bounding the number of membranes and leaving free the quantity of energy associated with each rule we have only generated all ma...
TL;DR: An improved convergence rates of standard backpropagation model with some modifications in its learning strategies is discussed, which is experimented on XOR problem, data of profitability analysis and Kuala Lumpur Composite Index and handwritten/handprinted digits.
Abstract: Most supervised neural networks are trained by minimizing the mean squared error of the training set. But there are problems of using mean squared error especially whenever the target output is equal to the actual output in which the error signal tends to zero. This will lead to the instability of the internal structure of the network as well. In this paper, we discuss an improved convergence rates of standard backpropagation model with some modifications in its learning strategies. A modified backpropagation model is experimented on XOR problem, data of profitability analysis and Kuala Lumpur Composite Index (KLCI) at Kuala Lumpur Stock Exchange (KLSE) and handwritten/handprinted digits. The results are compared with standard backpropagation model which is based on mean square errors
TL;DR: A new algebraic multigrid solution strategy for large linear systems with a sparse matrix arising from a finite element discretization of some self-adjoint, second order, scalar, elliptic partial differential equation is presented.
Abstract: This paper presents a new algebraic multigrid (AMG) solution strategy for large linear systems with a sparse matrix arising from a finite element discretization of some self-adjoint, second order, scalar, elliptic partial differential equation. The AMG solver is based on Ruge/Stubens method. Ruge/Stubens algorithm is robust for M-matrices, but unfortunately the “region of robustness“ between symmetric positive definite M-matrices and general symmetric positive definite matrices is very fuzzy. For this reason the so-called element preconditioning technique is introduced in this paper. This technique aims at the construction of an M-matrix that is spectrally equivalent to the original stiffness matrix. This is done by solving small restricted optimization problems. AMG applied to the spectrally equivalent M-matrix instead of the original stiffness matrix is then used as a preconditioner in the conjugate gradient method for solving the original problem. The numerical experiments show the efficiency and the r...
TL;DR: In this article, the authors applied the iterative transformation method to the numerical solution of the sequence of free boundary problems obtained from one-dimensional parabolic moving boundary problems via the implicit Euler's method.
Abstract: The main contribution of this paper is the application of the iterative transformation method to the numerical solution of the sequence of free boundary problems obtained from one-dimensional parabolic moving boundary problems via the implicit Euler's method. The combination of the two methods represents a numerical approach to the solution of those problems. Three parabolic moving boundary problems, two with explicit and one with implicit moving boundary conditions, are solved in order to test the validity of the proposed approach. As far as the moving boundary position is concerned the obtained numerical results are found to be in agreement with those available in literature.
TL;DR: The investigation undertaken in this study reveals that the extended fourth order RK methods based on AM, and CeM suit well for the system of Initial Value Problems (IVPs).
Abstract: Extended fourth order Runge-Kutta (RK) formulae based on Arithmetic Mean (AM), Geometric Mean (GM), Harmonic Mean (HaM), Heronian Mean (HeM), Root Mean Square (RM), Centroidal Mean (CeM) and Contraharmonic Mean (CoM) are developed to solve the system of linear differential equations.The accuracy of the new formulae are tested for five major Initial Value Problems (IVPs) from the real world applications.The algorithms governing the methods can easily be computerized.The investigation undertaken in this study reveals that the extended fourth order RK methods based on AM, and CeM suit well for the system of Initial Value Problems (IVPs).
TL;DR: A new algorithm of O(h 4) is reported for the numerical solution of ux and uy for the solution of two dimensional quasi-linear elliptic equation subject to the Dirichlet boundary conditions and requires only nine grid points on a uniform square grid.
Abstract: We report a new algorithm of O(h 4) for the numerical solution of ux and uy for the solution of two dimensional quasi-linear elliptic equation subject to the Dirichlet boundary conditions. The proposed method requires only nine grid points on a uniform square grid and applicable to the problems both in cartesian and polar coordinates. We also discuss two sets of fourth-order finite difference methods; one in the absence of mixed derivative term, second when the coefficient of uxy is not equal to zero and the coefficients of uxx and u yy are equal. There do not exist fourth order finite difference schemes involving nine grid points for the general case. Numerical examples are given to illustrate the method and its fourth order convergence.
TL;DR: Some difference schemes for singularly perturbed two point boundary value problems are derived using spline in compression using second order accurate schemes.
Abstract: Some difference schemes for singularly perturbed two point boundary value problems are derived using spline in compression. These schemes are second order accurate. Numerical examples are given in support of the theoretical results.
TL;DR: An explicit method for solving a first order wave equation is treated and the stability condition and comparison between the considered method and Lax-Wendroff method are discussed.
Abstract: Restrictive Taylor approximation is a new approach similar to Restrictive Pade' approximation mentioned in [2] is proposed. An explicit method for solving a first order wave equation is treated. The suggested method is of high accuracy whatever the exact solution is too large. It treats also the discontinuous behavior of the initial data for the function or its derivative. The stability condition and comparison between the considered method and Lax-Wendroff method are discussed.
TL;DR: A double Legendre spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomo-geneous mixed boundary conditions are presented.
Abstract: We present a double Legendre spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomo-geneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. One numerical application of how to use these methods is described. Numerical results obtained compare favorably with those of the analytical solution. Accurate double Legendre spectral approximations for Poisson' and Helmholtz' equations are also noted.
TL;DR: The notions of density, thinness, residue and ideal in a free monoid can all be expressed in terms of the infix order and the same notions with respect to arbitrary binary relations are introduced.
Abstract: The notions of density, thinness, residue and ideal in a free monoid can all be expressed in terms of the infix order. Guided by these definitions we introduce the same notions with respect to arbitrary binary relations. We then investigate properties of these generalized notions and explore the connection to the theory of codes. We show that, under certain assumptions about the relation, density is preserved by an endomorphism or the inverse of an endomorphism if and only if-essentially-the endomorphism induces a permutation of the generators of the free monoid.
TL;DR: Find the longest upsequence (resp. longest downsequence) of a permutation solves the maxi- mum independent set problem for the corresponding permutation graph and discusses the problem of efficiently constructing the Young tableau for a given permutation.
Abstract: Given a permutation of n numbers, its longest upsequence can be found in time O(nlog logn). Finding the longest upsequence (resp. longest downsequence) of a permutation solves the maxi- mum independent set problem (resp. the clique problem)for the corresponding permuta- tion graph. Moreover, we discuss the problem of efficiently constructing the Young tableau for a given permutation.
TL;DR: A set of inverse perspective equations for reconstruction of a line in 3-D space based on coplanarity equations is derived based on the correspondence between the pair of projections of the line on the image planes and the effect of noise and parameters of imaging setup, on errors in reconstruction.
Abstract: The process of reconstruction of a line in 3-D space from a pair of arbitrary perspective views obtains the set of parameters representing the line. This method is widely used in many applications of 3-D object recognition and machine inspection. However in certain applications which require a large degree of accuracy, a study of errors in the process of reconstruction, with the help of a rigorous performance analysis is necessary. In this paper we derive a set of inverse perspective equations for reconstruction of a line in 3-D space based on coplanarity equations. We assume the correspondence between the pair of projections of the line on the image planes. Simulation studies were conducted to observe the effect of noise on errors in the process of reconstruction. We present this performance analysis illustrating the effect of noise and parameters of imaging setup, on errors in reconstruction. Smaller resolution of the image, certain geometric conditions of the line and imaging setup produce poor perform...
TL;DR: It is proved that, after the application of Kovarik's algorithm, both rows and columns of the matrix are transformed in vectors which are “quasi-orthogonal”, in a sense that is clearly described.
Abstract: In [5] Kovarik described a method for approximate orthogonalization of a finite set of linearly independent vectors from an arbitrary Hubert space. In this paper we generalize this method to the case when the vectors are rows (not necessary linearly independent) of an arbitrary rectangular real matrix. In this case we prove that, after the application of Kovarik's algorithm, both rows and columns of the matrix are transformed in vectors which are “quasi-orthogonal”, in a sense that is clearly described. Some numerical experiments, on a matrix obtained from the discretization of a first kind integral equation are presented in the last section of the paper.
TL;DR: The basis of analysis of the finite difference equation considered here is the modified equivalent partial differential equation approach, developed from the 1974 work of Warming and Hyeet, which allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference methods.
Abstract: An inverse problem concerning the two-dimensional diffusion equation with source control parameter is considered. Four finite-difference schemes are presented for identifying the con- trol parameter which produces, at any given time, a desired energy distribution in a portion of the spatial domain. The fully explicit schemes developed for this purpose, are based on the (1,5) forward time centred space (FTCS) explicit formula, and the (1,9) FTCS scheme, are economical to use, are second-order and have bounded range of stability. Therange of stability for the 9-point finite difference scheme is less restrictive than the (1,5) FTCS formula. The fully implicit finite difference schemes employed, are based on the (5,1) backward time centred space (BTCS) formula, and the (5,5) Crank–Nicolson implicit scheme, which are unconditionally stable, but use more CPU times than the fully explicit techniques. The basis of analysis of the finite difference equation considered here is the modified equivalent partial differ...
TL;DR: The necessary and sufficient solvability conditions for the mixed LS-TLS problem in Frobenius norm are studied and the solution set, the minimum Frobenia norm solution and an algorithm to obtain the solution are given.
Abstract: Although the least squares (LS) problem and the total least squares (TLS) problem have received much attention, the mixed LS-TLS problem still remains to be investigated. In this paper, we study the necessary and sufficient solvability conditions for the mixed LS-TLS problem in Frobenius norm. The solution set, the minimum Frobenius norm solution and an algorithm to obtain the solution are also given. Further we propose the mixed LS-TLS problem in spectral norm and present the solvability condition.
TL;DR: It is shown that the (point) SOR method applied to the positive real system is convergent if the overrelaxiation parameter ω is in (0,ω U ); the upper bound ω U is also given in terms of the norm and smallest eigenvalue of related matrices.
Abstract: In this paper a new iterative method is given for the linear system of equations Au = b, where A is large, sparse and nonsymmetrical and AT + A is symmetric and positive definite (SPD) or equivalently A is positive real. The new iterative method is based on a mixed-type splitting of the matrix A. The iterative method contains an auxiliary matrix D 1. It is shown that by proper chxoice of D 1 the new iterative method is convergent. It is also shown that by special choice of D 1, the new iterative method becomes the well-known (point) successive overrelaxiation (SOR) [1] method. Hence, it is shown that the (point) SOR method applied to the positive real system is convergent if the overrelaxiation parameter ω is in (0,ω U ). The upper bound ω U is also given in terms of the norm and smallest eigenvalue of related matrices (see Eq. (23)).
TL;DR: A multilevel averaging weight method for one-dimensional dynamic load imbalance problems arising from the parallel Lagrange numerical simulation of multiple matters non-steady fluid dynamics is presented, which is suitable for both synchronous and heterogeneous parallel computing environments.
Abstract: A multilevel averaging weight method for one-dimensional dynamic load imbalance problems arising from the parallel Lagrange numerical simulation of multiple matters non-steady fluid dynamics is presented in this paper, which is suitable for both synchronous and heterogeneous parallel computing environments. The theoretical analysis for the robustness of this method and the parallel numerical experiments with two parallel machines are also given.
TL;DR: This scheme has a fourth order accuracy when the perturbation parameter, ϵ is fixed and is presented as an exponentially scheme for solving singularly perturbed Volterra integro-differ-ential equations.
Abstract: We present an exponentially scheme for solving singularly perturbed Volterra integro-differ-ential equations. This scheme has a fourth order accuracy when the perturbation parameter, e is fixed. Stability analysis of this scheme is discussed. Numerical results and comparisons to other schemes are given.
TL;DR: A numerical algorithm which is based on the representation of the theoretical solution by a perturbation of a polynomial interpolating function with an exponential function is proposed which is stable, consistent and convergent.
Abstract: In this paper, we propose a numerical algorithm which is based on the representation of the theoretical solution by a perturbation of a polynomial interpolating function with an exponential function. The numerical algorithm is stable, consistent and convergent. Some numerical results were obtained to illustrate the accuracy of the algorithm.
TL;DR: Stability measures of a communication network are defined and the stability measures of some static interconnection networks which are known long times and w-star networks that are a new graph class, are given.
Abstract: It is important that a communication service has to service dependability by high level. Many affairs cause failures in a network. Destroying nodes or links in communication network, cable cuts, node interruptions, software errors or hardware failures and transmission failure at various points, human error or accident and can interrupt service for long periods of time. At the beginning a communication network, requiring greater degree of stability or less vulnerability. In this work, various stability measures of a communication network are defined and the stability measures of some static interconnection networks which are known long times and w-star networks that are a new graph class, are given.