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Tests of probabilistic models for propagation of roundoff errors
Communications of the ACM, 1966In any prolonged computation it is generally assumed that the accumulated effect of roundoff errors is in some sense statistical. The purpose of this paper is to give precise descriptions of certain probabilistic models for roundoff error, and then to describe a series of experiments for testing the validity of these models.
T E Hull
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Roundoff errors in block-floating-point systems
IEEE Transactions on Signal Processing, 1996Block-floating-point representation is a special case of floating-point representation, where several numbers have a joint exponent term. In this paper, roundoff errors in signal processing systems utilizing block-floating-point representation are studied. Special emphasis is on analysis of quantization errors when data is quantized to a block-floating-
Jaakko T Astola
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An approach to eliminate roundoff errors in digital filters
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1979"Second-order quantizers" are introduced which can be used for implementing recursive digital filters with practically no roundoff errors or limit-cycle oscillations. Based on the idea of changing the transfer function used to compute roundoff errors, these quantizers save the low-order bits to correct the product at future iterations. For several pole
A Abu-El-Haija
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On Local Roundoff Errors in Floating-Point Arithmetic
Journal of the ACM, 1973 A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator.
Toyohisa Kaneko, Bede Liu
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Roundoff errors for polynomial evaluation by a family of formulae
Computing, 2008 The classical Lagrange interpolation formula is rewritten in the barycentric form. The authors show that these kind of formulas can be analyzed by making a distinction between the first steps corresponding to computations to high relative accuracy and the final sum, where high relative accuracy cannot be ensured.
Jesús M. Carnicer +2 more
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Interval Enclosures of Upper Bounds of Roundoff Errors Using Semidefinite Programming
ACM Transactions on Mathematical Software, 2018 18 pages, 2 tables, 1 figureInternational audienceA longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors.
Víctor Magron
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On Roundoff Error Growth in Elliptic Problems
ACM Transactions on Mathematical Software, 2018Large-scale linear systems arise in finite-difference and finite-element discretizations of elliptic problems. With increasing computer performance, ever larger systems are solved using direct methods. How large can such systems be without roundoff compromising accuracy? Here we model roundoff dynamics in standard LU
Ivo Babuska, Gustaf Söderlind
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Algorithms for roundoff error analysis —A relative error approach
Computing, 1980Methods are presented for performing various error analyses of numerical algorithms. These analyses include forward, backward, and B-analysis (a combination of forward and backward). These analyses additionally provide alternative criteria by which different algorithms that solve the same problem may be compared.
John L. Larson, Ahmed H. Sameh
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On the statistics of fixed-point roundoff error
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1985Roundoff error after fixed-point multiplication is commonly modeled as uniformly distributed white noise that is uncorrelated with the signal. This paper presents a statistical analysis of fixed-point roundoff error that identifies the conditions under which this model is valid, and examines the statistical behavior of roundoff error when these ...
Casper W. Barnes +2 more
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