Software for Roundoff Analysis

Miller, Webb; Wrathall, Celia

doi:10.1016/b978-0-12-497250-6.50007-8

Cited by 19 publications

(39 citation statements)

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“…[9] highlights those portions of a priori roundoff error analysis which can possibly be automated. More specific attempts are those which aim at developing software for error analysis in a numerical computational setting [10], [11], [12] and [13]. As regards algebraic computing, the concept of error analysis based on computer algebra system (CAS) for differential error-propagation model is introduced in [14].…”

Section: Introductionmentioning

confidence: 99%

On the Dimensional Estimate of Rounding-Errors of a typical Computing Process

Danial

Noor²,

Usmani

et al. 2007

2007 IEEE International Multitopic Conference

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The phenomenon of roundoff-error propagation is a well known problem in computations involving floating point arithmetic. Prominent works in the field of error analysis include (1) the error-analysis based on differential error-propagation model for computer algebra system (CAS), (2) the identification and reformulation of instability in a code generated by CAS, (3) estimating the bounds on errors in symbolic and numerical environments. The main concern in these attempts is to control error-propagation by using numerically stable code. Beside these attempts, only few efforts are made towards the theoretical understanding of the underlying process of error propagation. In this paper, we attempt to show that the roundoff-errors may propagate as a random-fractal process. We apply concepts of nonlinear time-series analysis on a series constituting successive roundoff-errors generated during the computation of Henon-map solutions. We estimate the correlation dimension, which is a measure of the fractal dimension, of the series as 5.5 ± 0.05. This low value of correlation dimension shows that the error series can be modeled by a low dimensional dynamical system.

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Section: Introductionmentioning

confidence: 99%

On the Dimensional Estimate of Rounding-Errors of a typical Computing Process

Danial

Noor²,

Usmani

et al. 2007

2007 IEEE International Multitopic Conference

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“…The view of the method developed b.y W. Miller [11,12,13] differs essentially from the idea of interval arithmetic. Rather than trying to approximate the interval where the result lies, a hilf-climbin 9 method is used to localize the worst possible initial data for an algorithm in the sense of the propagation of rounding errors.…”

Section: Introductionmentioning

confidence: 99%

Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms

Linnainmaa

1983

BIT

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Abstract.After introducing briefly the principles of the error linearization method, which is able to determine the coefficients of the first order error approximation, a collection of examples is presented to demonstrate its efficiency as a test bench tbr analyzing numerical algorithms. These examples illustrate the propagation of initial errors, the effect of cancellation, the easy location of the most unstable parts of an algorithm, calculation of condition numbers, approximating the statistical behavior of accumulated errors and the convergence of iterative methods.

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“…Under the first topic above, we investigate here conditions on a graph that wdl guarantee insensitivity of its error behavior to changes in the model. Our motivation is as follows: Rounding error analysis is being brought within reach of the nonspecialist by the development of software packages [ 11,12] that automatically perform many such analyses using the above error model. Delivery of this capability to users unaware of the idealizations in the crude underlying model greatly increases the danger of numerical instability being diagnosed when, in fact, the numerical method being tested is relatively insensitive to errors that can actually occur, but highly sensitive to the sorts of errors fabricated by the particular error model.…”

Section: Introductionmentioning

confidence: 99%

Reducibility Among Floating-Point Graphs

Johnson

Miller

Minnihan

et al. 1979

J. ACM

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The graph-theoretical models of this paper can be used to compare the rounding error behavior of numerical programs The models follow the approach, popularized by Wilkinson, of assuming independent rounding errors at each arithmetic operation Models constructed on th~s assumpuon are more tractable than would be the case under more realistic assumptions There are identified two easily tested condmons on programs which guarantee that" error analyses are relatively lnsensmve to the particular graph model employed The development has the addmonal benefit of sometimes providing an elementary proof that one program is comparable in stablhty to another Examples of such results are gwen KEY WORDS AND PHRASES rounding errors, numerical stability, arithmetic graphs CR CATEGORIES 5 11, 5 14

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Software for Roundoff Analysis

Cited by 19 publications

References 0 publications

On the Dimensional Estimate of Rounding-Errors of a typical Computing Process

On the Dimensional Estimate of Rounding-Errors of a typical Computing Process

Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms

Reducibility Among Floating-Point Graphs

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