Control-Theoretic Forward Error Analysis of Iterative Numerical Algorithms

2013 ◽  
Vol 58 (6) ◽  
pp. 1524-1529 ◽  
Author(s):  
Ammar Hasan ◽  
Eric C. Kerrigan ◽  
George A. Constantinides
Keyword(s):  
Error Analysis ◽  
Numerical Algorithms ◽  
Forward Error

scholarly journals A Note on the Perturbation of arithmetic expressions

2016 ◽  
Vol 13 (1) ◽  
pp. 190-197
Author(s):  
Baghdad Science Journal
Keyword(s):  
Error Analysis ◽  
Gaussian Elimination ◽  
Effective Means ◽  
Numerical Algorithms ◽  
Posteriori Error ◽  
Condition Numbers ◽  
A Posteriori ◽  
Rounding Errors ◽  
A Posteriori Error ◽  
Forward Error

In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a priori and a posteriori error analysis.

Forward error analysis of gaussian elimination

1985 ◽  
Vol 46 (3) ◽  
pp. 365-395 ◽  
Author(s):  
Friedrich Stummel
Keyword(s):  
Error Analysis ◽  
Gaussian Elimination ◽  
Forward Error

scholarly journals Applying Computer Algebra Systems in Approximating the Trigonometric Functions

2018 ◽  
Vol 23 (3) ◽  
pp. 37 ◽  
Author(s):  
Le Quan ◽  
Thái Nhan
Keyword(s):  
Error Analysis ◽  
Computer Algebra ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Computer Algebra Systems ◽  
Trigonometric Functions ◽  
Modern Computer ◽  
Sine And Cosine Functions ◽  
Cosine Functions ◽  
Very High

We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor’s expansion about a point having a form of kp, k∈Z and p=π/2, and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximating π with a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the use of algorithms. Numerical and graphical results are implemented by MAPLE.

scholarly journals Numerical Algorithms for Computing Eigenvalues of Discontinuous Dirac System Using Sinc-Gaussian Method

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. H. Bhrawy ◽  
M. M. Tharwat ◽  
A. Al-Fhaid
Keyword(s):  
Error Analysis ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Transmission Conditions ◽  
Numerical Results ◽  
New Method ◽  
Dirac System ◽  
Sinc Method ◽  
Dirac Systems ◽  
Gaussian Method

The eigenvalues of a discontinuous regular Dirac systems with transmission conditions at the point of discontinuity are computed using the sinc-Gaussian method. The error analysis of this method for solving discontinuous regular Dirac system is discussed. It shows that the error decays exponentially in terms of the number of involved samples. Therefore, the accuracy of the new method is higher than the classical sinc-method. Numerical results indicating the high accuracy and effectiveness of these algorithms are presented. Comparisons with the classical sinc-method are given.

Empirical Similarity Analysis Using Adaptive Trigonometric Functions

2009 ◽  
Author(s):  
Srikanth Tadepalli ◽  
Kristin L. Wood
Keyword(s):  
Experimental Data ◽  
Error Analysis ◽  
Complex Systems ◽  
Drag Coefficient ◽  
Engineering Design ◽  
Numerical Algorithms ◽  
Similarity Analysis ◽  
Trigonometric Functions ◽  
Numerical Approximations ◽  
Prediction Parameters

Similarity methods have been widely employed in engineering design and analysis to model and scale complex systems. The Empirical Similitude Method (ESM) is one such method based on the use of experimental data. Using a variant of the similitude process involving experimental data, we present in this paper, the use of advanced numerical approximations, trigonometric functions in particular to model and predict the performance of design artifacts. Specifically, an airfoil design is modeled, and the values of the drag coefficient are estimated based on the advanced ESM. Intermediate test specimens are used to correlate experimental data to produce the required prediction parameters. Mathematical development and error analysis are also elaborated by delving into continuity and adaptivity features of numerical algorithms.

scholarly journals Accurate Evaluation of Polynomials in Legendre Basis

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Peibing Du ◽  
Hao Jiang ◽  
Lizhi Cheng
Keyword(s):  
Error Analysis ◽  
Numerical Experiments ◽  
Floating Point ◽  
Polynomial Evaluation ◽  
Accurate Evaluation ◽  
Forward Error ◽  
Floating Point Numbers

This paper presents a compensated algorithm for accurate evaluation of a polynomial in Legendre basis. Since the coefficients of the evaluated polynomial are fractions, we propose to store these coefficients in two floating point numbers, such as double-double format, to reduce the effect of the coefficients’ perturbation. The proposed algorithm is obtained by applying error-free transformation to improve the Clenshaw algorithm. It can yield a full working precision accuracy for the ill-conditioned polynomial evaluation. Forward error analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm.

scholarly journals Numerical Solutions of Fuzzy Differential Equations by Taylor Method

2002 ◽  
Vol 2 (2) ◽  
pp. 113-124 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Tofigh Allah Viranloo
Keyword(s):  
Differential Equations ◽  
Error Analysis ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Numerical Algorithms ◽  
Cauchy Problems ◽  
Linear And Nonlinear ◽  
Taylor Method

Abstract In this paper, numerical algorithms for solving “fuzzy ordinary differential equations” are considered. A scheme based on the Taylor method of order p is discussed in detail and this is followed by a complete error analysis. The algorithm is illustrated by solving some linear and nonlinear fuzzy Cauchy problems.

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