Abstract: This paper describes the Message Passing Interface
(MPI) implementation of ADETRAN language, and its evaluation
on SX-ACE supercomputers. ADETRAN language includes pdo
statement that specifies the data distribution and parallel computations
and pass statement that specifies the redistribution of arrays. Two
methods for implementation of pass statement are discussed and the
performance evaluation using Splitting-Up CG method is presented.
The effectiveness of the parallelization is evaluated and the advantage
of one dimensional distribution is empirically confirmed by using the
results of experiments.
Abstract: In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally, we give a numerical example to confirm our theoretical results.
Abstract: We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.
Abstract: Linear systems are widely used in many fields of science and engineering. In many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. Therefore it is important to perform numerical algorithms or procedures that would treat general fuzzy linear systems and solve them using iterative methods. This paper aims are to solve fuzzy linear systems using four types of Jacobi based iterative methods. Four iterative methods based on Jacobi are used for solving a general n × n fuzzy system of linear equations of the form Ax = b , where A is a crisp matrix and b an arbitrary fuzzy vector. The Jacobi, Jacobi Over-Relaxation, Refinement of Jacobi and Refinement of Jacobi Over-Relaxation methods was tested to a five by five fuzzy linear system. It is found that all the tested methods were iterated differently. Due to the effect of extrapolation parameters and the refinement, the Refinement of Jacobi Over-Relaxation method was outperformed the other three methods.
Abstract: In this paper, we discuss semiconvergence of the alternating iterative methods for solving singular systems. The semiconvergence theories for the alternating methods are established when the coefficient matrix is a singular matrix. Furthermore, the corresponding comparison theorems are obtained.
Abstract: We study the semiconvergence of Gauss-Seidel iterative
methods for the least squares solution of minimal norm of rank
deficient linear systems of equations. Necessary and sufficient conditions
for the semiconvergence of the Gauss-Seidel iterative method
are given. We also show that if the linear system of equations is
consistent, then the proposed methods with a zero vector as an initial
guess converge in one iteration. Some numerical results are given to
illustrate the theoretical results.
Abstract: A generalized Dirichlet to Neumann map is
one of the main aspects characterizing a recently introduced
method for analyzing linear elliptic PDEs, through which it
became possible to couple known and unknown components
of the solution on the boundary of the domain without
solving on its interior. For its numerical solution, a well conditioned
quadratically convergent sine-Collocation method
was developed, which yielded a linear system of equations
with the diagonal blocks of its associated coefficient matrix
being point diagonal. This structural property, among others,
initiated interest for the employment of iterative methods for
its solution. In this work we present a conclusive numerical
study for the behavior of classical (Jacobi and Gauss-Seidel)
and Krylov subspace (GMRES and Bi-CGSTAB) iterative
methods when they are applied for the solution of the Dirichlet
to Neumann map associated with the Laplace-s equation
on regular polygons with the same boundary conditions on
all edges.
Abstract: For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.
Abstract: The spectral action balance equation is an equation that
used to simulate short-crested wind-generated waves in shallow water
areas such as coastal regions and inland waters. This equation consists
of two spatial dimensions, wave direction, and wave frequency which
can be solved by finite difference method. When this equation with
dominating convection term are discretized using central differences,
stability problems occur when the grid spacing is chosen too coarse.
In this paper, we introduce the splitting upwind schemes for avoiding
stability problems and prove that it is consistent to the upwind scheme
with same accuracy. The splitting upwind schemes was adopted
to split the wave spectral action balance equation into four onedimensional
problems, which for each small problem obtains the
independently tridiagonal linear systems. For each smaller system
can be solved by direct or iterative methods at the same time which
is very fast when performed by a multi-processor computer.
Abstract: An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.
Abstract: In the present work, we propose a new method for
solving the matrix equation AXB=F . The new method can
be considered as a generalized form of the well-known global full
orthogonalization method (Gl-FOM) for solving multiple linear
systems. Hence, the method will be called extended Gl-FOM (EGl-
FOM). For implementing EGl-FOM, generalized forms of block
Krylov subspace and global Arnoldi process are presented. Finally,
some numerical experiments are given to illustrate the efficiency of
our new method.
Abstract: In this note, we consider a family of iterative formula for computing the weighted Minskowski inverses AM,N in Minskowski space, and give two kinds of iterations and the necessary and sufficient conditions of the convergence of iterations.
Abstract: Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.
Abstract: This study proposes a multi-response surface
optimization problem (MRSOP) for determining the proper choices
of a process parameter design (PPD) decision problem in a noisy
environment of a grease position process in an electronic industry.
The proposed models attempts to maximize dual process responses
on the mean of parts between failure on left and right processes. The
conventional modified simplex method and its hybridization of the
stochastic operator from the hunting search algorithm are applied to
determine the proper levels of controllable design parameters
affecting the quality performances. A numerical example
demonstrates the feasibility of applying the proposed model to the
PPD problem via two iterative methods. Its advantages are also
discussed. Numerical results demonstrate that the hybridization is
superior to the use of the conventional method. In this study, the
mean of parts between failure on left and right lines improve by
39.51%, approximately. All experimental data presented in this
research have been normalized to disguise actual performance
measures as raw data are considered to be confidential.
Abstract: In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.
Abstract: In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.
Abstract: Based on the fuzzy set theory this work develops two
adaptations of iterative methods that solve mathematical programming
problems with uncertainties in the objective function and in
the set of constraints. The first one uses the approach proposed by
Zimmermann to fuzzy linear programming problems as a basis and
the second one obtains cut levels and later maximizes the membership
function of fuzzy decision making using the bound search method.
We outline similarities between the two iterative methods studied.
Selected examples from the literature are presented to validate the
efficiency of the methods addressed.
Abstract: In a previous work, we presented the numerical
solution of the two dimensional second order telegraph partial
differential equation discretized by the centred and rotated five-point
finite difference discretizations, namely the explicit group (EG) and
explicit decoupled group (EDG) iterative methods, respectively. In
this paper, we utilize a domain decomposition algorithm on these
group schemes to divide the tasks involved in solving the same
equation. The objective of this study is to describe the development
of the parallel group iterative schemes under OpenMP programming
environment as a way to reduce the computational costs of the
solution processes using multicore technologies. A detailed
performance analysis of the parallel implementations of points and
group iterative schemes will be reported and discussed.
Abstract: The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.
Abstract: Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the
root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which
is to some extent like the secant method, is accompanied with some
numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically
iterative schemes.