scholarly journals Generalizations of Nekrasov matrices and applications

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Ljiljana Cvetković ◽  
Vladimir Kostić ◽  
Maja Nedović
Keyword(s):  
Inverse Matrix ◽  
Index Set ◽  
Main Motivation ◽  
Numerical Examples ◽  
Nekrasov Matrices ◽  
The Given

AbstractIn this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already calculated in order to conclude that the given matrix is nonsingular. Also, we present new max-norm bounds for the inverse matrix and illustrate these results by numerical examples, comparing the results to some already known bounds for Nekrasov matrices.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

CONTROL OF STEADY-STATE VIBRATIONS OF RECTANGULAR PLATES

2011 ◽  
Vol 11 (03) ◽  
pp. 535-562 ◽  
Author(s):  
K. A. ALSAIF ◽  
M. A. FODA
Keyword(s):  
Steady State ◽  
Function Method ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Selected Lines ◽  
Numerical Examples ◽  
Nodal Lines ◽  
Free And Forced Vibrations ◽  
Concentrated Masses ◽  
The Given

The focus of the present research is to eliminate the undesired steady-state vibrations at selected lines or locations in a vibrating plate by means of adding attachments at arbitrary selected locations. These attachments can be either added concentrated masses and/or translational or rotational springs which are connected to the plate at one end and grounded at the other. The case of attachment of translational and/or rotational oscillators systems is examined. In addition, imposing lines of zero displacements (nodal lines) at selected locations are also investigated. The dynamic Green's function method is employed. Several numerical examples are cited to verify the utility of the proposed method. In addition, sample experiments to measure the plate free and forced vibrations for the given boundary conditions are conducted and the experimental measurements are compared with the analytical results.

scholarly journals A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Alicia Cordero ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Fourth Order ◽  
Order Of Convergence ◽  
Nonsmooth Equations ◽  
Order Convergence ◽  
Linear Combinations ◽  
Numerical Examples ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Seventh Order ◽  
The Given

A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.6266. Also, numerical examples are used to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other derivative-free methods, including some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture.

scholarly journals Data Visualization Using Rational Trigonometric Spline

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Uzma Bashir ◽  
Jamaludin Md. Ali
Keyword(s):  
Data Visualization ◽  
The Other ◽  
Shape Features ◽  
Shape Parameters ◽  
Shape Preserving ◽  
Numerical Examples ◽  
Data Points ◽  
Trigonometric Spline ◽  
The Given

This paper describes the use of trigonometric spline to visualize the given planar data. The goal of this work is to determine the smoothest possible curve that passes through its data points while simultaneously satisfying the shape preserving features of the data. Positive, monotone, and constrained curve interpolating schemes, by using aC1piecewise rational cubic trigonometric spline with four shape parameters, are developed. Two of these shape parameters are constrained and the other two are set free to preserve the inherited shape features of the data as well as to control the shape of the curve. Numerical examples are given to illustrate the worth of the work.

scholarly journals Solving Nonsmooth Equations Using Derivative-Free Methods

2012 ◽  
Vol 3 ◽  
pp. 37-45
Author(s):  
M.S.M. Bahgat ◽  
M.A. Hafiz
Keyword(s):  
Error Analysis ◽  
Nonlinear Equations ◽  
Divided Differences ◽  
Nonsmooth Equations ◽  
Linear Combinations ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
The Given

In this paper, a family of derivative-free methods of cubic convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.442. The convergence and error analysis are given. Also, numerical examples are used to show the performance of the presented methods and to compare with other derivative-free methods. And, were applied these methods on smooth and nonsmooth equations.

scholarly journals Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices

2015 ◽  
Vol 12 ◽  
pp. 1-13
Author(s):  
R. Purushothaman Nair
Keyword(s):  
Vandermonde Matrix ◽  
Inverse Matrix ◽  
Identity Matrix ◽  
Vandermonde Matrices ◽  
The Matrix ◽  
Matrix Transforms ◽  
The Given ◽  
Zero Vector

A non-unit bidiagonal matrix and its inverse with simple structures are introduced. These matrices can be constructed easily using the entries of a given non-zero vector without any computations among the entries. The matrix transforms the given vector to a column of the identity matrix. The given vector can be computed back without any round off error using the inverse matrix. Since a Vandermonde matrix can also be constructed using given n quantities, it is established in this paper that Vandermonde matrices can be factorized in a simple way by applying these bidiagonal matrices. Also it is demonstrated that factors of Vandermonde and inverse Vandermonde matrices can be conveniently presented using the matrices introduced here.

scholarly journals Note on subdirect sums of $ \{i_0\} $-Nekrasov matrices

2021 ◽  
Vol 7 (1) ◽  
pp. 617-631
Author(s):  
Jing Xia ◽  
Keyword(s):  
Scientific Computing ◽  
Sufficient Conditions ◽  
Numerical Examples ◽  
Direct Sum ◽  
Nekrasov Matrices

<abstract><p>The concept of $ k $-subdirect sums of matrices, as a generalization of the usual sum and the direct sum, plays an important role in scientific computing. In this paper, we introduce a new subclass of $ S $-Nekrasov matrices, called $ \{i_0\} $-Nekrasov matrices, and some sufficient conditions are given which guarantee that the $ k $-subdirect sum $ A\bigoplus_k B $ is an $ \{i_0\} $-Nekrasov matrix, where $ A $ is an $ \{i_0\} $-Nekrasov matrix and $ B $ is a Nekrasov matrix. Numerical examples are reported to illustrate the conditions presented.</p></abstract>

scholarly journals Relational Fuzzy c-Means and Kernel Fuzzy c-Means Using an Object-Wise β-Spread Transformation

2013 ◽  
Vol 17 (4) ◽  
pp. 511-519 ◽  
Author(s):  
Yuchi Kanzawa ◽  
Keyword(s):  
Positive Semidefinite ◽  
Relational Data ◽  
Gram Matrix ◽  
Clustering Methods ◽  
Numerical Examples ◽  
Fuzzy C Means ◽  
Indefinite Kernel ◽  
Conventional Methods ◽  
The Given ◽  
Better Than

Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β-spread transformation was proposed for such cases, which modified a given set of relational data or a give a kernel Gram matrix such that the modified β value is common to all objects. In this paper, we propose an object-wise β-spread transformation for use in both relational and kernelized fuzzy c-means clustering. The proposed system retains the given data better than conventional methods, and numerical examples show that our method is efficient for both relational and kernel fuzzy c-means.

scholarly journals Fast fixed-time synchronization of T–S fuzzy complex networks

2021 ◽  
Vol 26 (4) ◽  
pp. 597-609
Author(s):  
Shuai Liu ◽  
Lingli Zhao ◽  
Wanli Zhang ◽  
Xinsong Yang ◽  
Fuad E. Alsaadi
Keyword(s):  
Complex Networks ◽  
Time Synchronization ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Analytical Techniques ◽  
Fixed Time ◽  
Comparison System ◽  
Numerical Examples ◽  
Control Schemes ◽  
The Given

In this paper, fast fixed-time (FDT) synchronization of T–S fuzzy (TSF) complex networks (CNs) is considered. The given control schemes can make the CNs synchronize with the given isolated system more fleetly than the most of existing results. By constructing comparison system and applying new analytical techniques, sufficient conditions are established to derive fast FDT synchronization speedily. In order to give some comparisons, FDT synchronization of the considered CNs is also presented by designing FDT fuzzy controller. Numerical examples are given to illustrate our new results.

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