Abstract: A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.
Abstract: Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.
Abstract: A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.
Abstract: This paper presents two simplified models to
determine nodal voltages in power distribution networks. These
models allow estimating the impact of the installation of reactive
power compensations equipments like fixed or switched capacitor
banks. The procedure used to develop the models is similar to the
procedure used to develop linear power flow models of transmission
lines, which have been widely used in optimization problems of
operation planning and system expansion. The steady state non-linear
load flow equations are approximated by linear equations relating the
voltage amplitude and currents. The approximations of the linear
equations are based on the high relationship between line resistance
and line reactance (ratio R/X), which is valid for power distribution
networks. The performance and accuracy of the models are evaluated
through comparisons with the exact results obtained from the
solution of the load flow using two test networks: a hypothetical
network with 23 nodes and a real network with 217 nodes.
Abstract: In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.
Abstract: In this paper, we investigate two parallel alternating methods for solving the system of linear equations Ax = b and give convergence theorems for the parallel alternating methods when the coefficient matrix is a nonsingular H-matrix. Furthermore, we give one example to show our results.
Abstract: In the present paper some recommendations for the
use of software package “Mathematica" in a basic numerical analysis
course are presented. The methods which are covered in the course
include solution of systems of linear equations, nonlinear equations
and systems of nonlinear equations, numerical integration,
interpolation and solution of ordinary differential equations. A set of
individual assignments developed for the course covering all the
topics is discussed in detail.
Abstract: This article presents a short discussion on
optimum neighborhood size selection in a spherical selforganizing
feature map (SOFM). A majority of the literature
on the SOFMs have addressed the issue of selecting optimal
learning parameters in the case of Cartesian topology SOFMs.
However, the use of a Spherical SOFM suggested that the
learning aspects of Cartesian topology SOFM are not directly
translated. This article presents an approach on how to
estimate the neighborhood size of a spherical SOFM based on
the data. It adopts the L-curve criterion, previously suggested
for choosing the regularization parameter on problems of
linear equations where their right-hand-side is contaminated
with noise. Simulation results are presented on two artificial
4D data sets of the coupled Hénon-Ikeda map.
Abstract: This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.
Abstract: In this paper, verified extension of the Ostrowski method which calculates the enclosure solutions of a given nonlinear equation is introduced. Also, error analysis and convergence will be discussed. Some implemented examples with INTLAB are also included to illustrate the validity and applicability of the scheme.
Abstract: Based on Traub-s methods for solving nonlinear
equation f(x) = 0, we develop two families of third-order
methods for solving system of nonlinear equations F(x) = 0. The
families include well-known existing methods as special cases.
The stability is corroborated by numerical results. Comparison
with well-known methods shows that the present methods are
robust. These higher order methods may be very useful in the
numerical applications requiring high precision in their computations
because these methods yield a clear reduction in number of iterations.
Abstract: An on-line condition monitoring method for transmission line is proposed using electrical circuit theory and IT technology in this paper. It is reasonable that the circuit parameters such as resistance (R), inductance (L), conductance (g) and capacitance (C) of a transmission line expose the electrical conditions and physical state of the line. Those parameters can be calculated from the linear equation composed of voltages and currents measured by synchro-phasor measurement technique at both end of the line. A set of linear voltage drop equations containing four terminal constants (A, B ,C ,D ) are mathematical models of the transmission line circuits. At least two sets of those linear equations are established from different operation condition of the line, they may mathematically yield those circuit parameters of the line. The conditions of line connectivity including state of connecting parts or contacting parts of the switching device may be monitored by resistance variations during operation. The insulation conditions of the line can be monitored by conductance (g) and capacitance(C) measurements. Together with other condition monitoring devices such as partial discharge, sensors and visual sensing device etc.,they may give useful information to monitor out any incipient symptoms of faults. The prototype of hardware system has been developed and tested through laboratory level simulated transmission lines. The test has shown enough evident to put the proposed method to practical uses.
Abstract: Most real world systems express themselves formally
as a set of nonlinear algebraic equations. As applications grow, the
size and complexity of these equations also increase. In this work, we
highlight the key concepts in using the homotopy analysis method
as a methodology used to construct efficient iteration formulas for
nonlinear equations solving. The proposed method is experimentally
characterized according to a set of determined parameters which
affect the systems. The experimental results show the potential and
limitations of the new method and imply directions for future work.
Abstract: In this paper, different approaches to solve the
forward kinematics of a three DOF actuator redundant hydraulic
parallel manipulator are presented. On the contrary to series
manipulators, the forward kinematic map of parallel manipulators
involves highly coupled nonlinear equations, which are almost
impossible to solve analytically. The proposed methods are using
neural networks identification with different structures to solve the
problem. The accuracy of the results of each method is analyzed in
detail and the advantages and the disadvantages of them in
computing the forward kinematic map of the given mechanism is
discussed in detail. It is concluded that ANFIS presents the best
performance compared to MLP, RBF and PNN networks in this
particular application.
Abstract: Phase-Contrast MR imaging methods are widely used
for measurement of blood flow velocity components. Also there are
some other tools such as CT and Ultrasound for velocity map
detection in intravascular studies. These data are used in deriving
flow characteristics. Some clinical applications are investigated
which use pressure distribution in diagnosis of intravascular disorders
such as vascular stenosis. In this paper an approach to the problem of
measurement of intravascular pressure field by using velocity field
obtained from flow images is proposed. The method presented in this
paper uses an algorithm to calculate nonlinear equations of Navier-
Stokes, assuming blood as an incompressible and Newtonian fluid.
Flow images usually suffer the lack of spatial resolution. Our
attempt is to consider the effect of spatial resolution on the pressure
distribution estimated from this method. In order to achieve this aim,
velocity map of a numerical phantom is derived at six different
spatial resolutions. To determine the effects of vascular stenoses on
pressure distribution, a stenotic phantom geometry is considered. A
comparison between the pressure distribution obtained from the
phantom and the pressure resulted from the algorithm is presented. In
this regard we also compared the effects of collocated and staggered
computational grids on the pressure distribution resulted from this
algorithm.