Forward error analysis of Gaussian elimination

1985 ◽  
Vol 46 (3) ◽  
pp. 397-415 ◽  
Author(s):  
Friedrich Stummel
Keyword(s):  
Error Analysis ◽  
Gaussian Elimination ◽  
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 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 Compensated Evaluation of Tensor Product Surfaces in CAGD

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2219
Author(s):  
Jorge Delgado Gracia
Keyword(s):  
Error Analysis ◽  
Tensor Product ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
De Casteljau Algorithm ◽  
Usual Form ◽  
Computer Aided ◽  
Forward Error ◽  
Polynomial Surface

In computer-aided geometric design, a polynomial surface is usually represented in Bézier form. The usual form of evaluating such a surface is by using an extension of the de Casteljau algorithm. Using error-free transformations, a compensated version of this algorithm is presented, which improves the usual algorithm in terms of accuracy. A forward error analysis illustrating this fact is developed.

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

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

Error Analysis in Neuropsychological Assessment of Verbal Memory and Learning

1995 ◽  
Vol 11 (1) ◽  
pp. 21-28 ◽  
Author(s):  
Dietmar Heubrock
Keyword(s):  
Error Analysis ◽  
Verbal Memory ◽  
Verbal Learning ◽  
Learning Disorders ◽  
Memory And Learning ◽  
Auditory Verbal Learning Test ◽  
Additional Information ◽  
Auditory Verbal Learning ◽  
Accurate Picture ◽  
Learning Test

Performance on a German version of the Rey Auditory-Verbal Learning Test (AVLT) was investigated for 64 juvenile patients who were subdivided in 6 clinical groups. In addition to standard evaluation of AVLT protocols which is usually confined to items recalled correctly, an error analysis was performed. Differentiating between total errors (TE), repetition errors (RE), and misnamings (ME), substantial differences between clinical groups could be demonstrated. It is argued that error analysis of verbal memory and learning enriches the understanding of neuropsychological syndromes, and provides additional information for diagnostic and clinical use. Thus, it is possible to gain a more accurate picture so that patients can be appropriately retrained, and research into the functional causes of memory and learning disorders can be intensified.

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