Quantization in Control Systems and Forward Error Analysis of Iterative Numerical Algorithms

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.

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An ISS and l-stability approach to forward error analysis of iterative numerical algorithms

49th IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc.2010.5717884 ◽

2010 ◽

Cited By ~ 2

Author(s):

Ammar Hasan ◽

Eric C. Kerrigan ◽

George A. Constantinides

Keyword(s):

Error Analysis ◽

Numerical Algorithms ◽

Forward Error

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Control-Theoretic Forward Error Analysis of Iterative Numerical Algorithms

IEEE Transactions on Automatic Control ◽

10.1109/tac.2012.2225513 ◽

2013 ◽

Vol 58 (6) ◽

pp. 1524-1529 ◽

Cited By ~ 7

Author(s):

Ammar Hasan ◽

Eric C. Kerrigan ◽

George A. Constantinides

Keyword(s):

Error Analysis ◽

Numerical Algorithms ◽

Forward Error

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Forward error analysis of gaussian elimination

Numerische Mathematik ◽

10.1007/bf01389492 ◽

1985 ◽

Vol 46 (3) ◽

pp. 365-395 ◽

Cited By ~ 3

Author(s):

Friedrich Stummel

Keyword(s):

Error Analysis ◽

Gaussian Elimination ◽

Forward Error

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Plant error analysis and compensation in adaptive cruise control systems

2012 15th International IEEE Conference on Intelligent Transportation Systems ◽

10.1109/itsc.2012.6338875 ◽

2012 ◽

Author(s):

Alexander D. Meadows ◽

Lingxi Li ◽

Yaobin Chen ◽

Glenn Widmann

Keyword(s):

Error Analysis ◽

Control Systems ◽

Adaptive Cruise Control ◽

Cruise Control

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Applying Computer Algebra Systems in Approximating the Trigonometric Functions

Mathematical and Computational Applications ◽

10.3390/mca23030037 ◽

2018 ◽

Vol 23 (3) ◽

pp. 37 ◽

Cited By ~ 2

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.

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

Abstract and Applied Analysis ◽

10.1155/2012/925134 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13 ◽

Cited By ~ 2

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.

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