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Stummel, F.

Perturbation theory for evaluation algorithms of arithmetic expressions. (English) Zbl 0515.65039

Math. Comput. 37, 435-473 (1981).
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Cited in 3 Reviews
Cited in 13 Documents

MSC:

65G50 Roundoff error
65F05 Direct numerical methods for linear systems and matrix inversion
65J05 General theory of numerical analysis in abstract spaces

Keywords:

rounding error analysis; evaluation algorithms; a priori and a posteriori error estimates; condition numbers; linear error equations; error propagation; forward analysis; backward analysis
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\textit{F. Stummel}, Math. Comput. 37, 435--473 (1981; Zbl 0515.65039)
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References:

[1] I. Babuška, Numerical Stability in Numerical Analysis, Proc. IFIP-Congress 1968, Amsterdam, North-Holland, Amsterdam, 1969, pp. 11-23.
[2] Ivo Babuška, Numerical stability in problems of linear algebra, SIAM J. Numer. Anal. 9 (1972), 53 – 77. · Zbl 0248.65026
[3] Ivo Babuška, Milan Práger, and Emil Vitásek, Numerical processes in differential equations, In cooperation with R. Radok. Translated from the Czech by Milada Boruvková, Státní Nakladatelství Technické Literatury, Prague; Interscience Publishers John Wiley & Sons, London-New York-Sydney, 1966. · Zbl 0156.16003
[4] F. L. Bauer, Genauigkeitsfragen bei der Lösung linearer Gleichungssysteme, Z. Angew. Math. Mech. 46 (1966), 409 – 421 (German). · Zbl 0148.39101
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[6] F. L. Bauer et al., Moderne Rechenanlagen, Chap. 3, Teubner, Stuttgart, 1964.
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[8] Peter Henrici, Elements of numerical analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1964. · Zbl 0149.10901
[9] John Larson and Ahmed Sameh, Efficient calculation of the effects of roundoff errors, ACM Trans. Math. Software 4 (1978), no. 3, 228 – 236. , https://doi.org/10.1145/355791.355794 John Larson, Errata: ”Efficient calculation of the effects of roundoff errors” (ACM Trans. Software 4 (1978), no. 3, 228 – 236) by Larson and A. Sameh, ACM Trans. Math. Software 5 (1979), no. 3, 372. · Zbl 0413.65037
[10] Seppo Linnainmaa, Taylor expansion of the accumulated rounding error, Nordisk Tidskr. Informationsbehandling (BIT) 16 (1976), no. 2, 146 – 160. · Zbl 0332.65024
[11] D. D. McCracken & W. S. Dorn, Numerical Methods and Fortran Programming, Wiley, New York, 1964. · Zbl 0139.12403
[12] Webb Miller, Software for roundoff analysis, ACM Trans. Math. Software 1 (1975), 108 – 128. · Zbl 0303.65036
[13] Webb Miller, Computer search for numerical instability, J. Assoc. Comput. Mach. 22 (1975), no. 4, 512 – 521. · Zbl 0345.65022
[14] Webb Miller and David Spooner, Software for roundoff analysis. II, ACM Trans. Math. Software 4 (1978), no. 4, 369 – 387. · Zbl 0399.65025
[15] John R. Rice, A theory of condition, SIAM J. Numer. Anal. 3 (1966), 287 – 310. · Zbl 0143.37101
[16] F. Stummel, Fehleranalyse numerischer Algorithmen, Lecture Notes, Univ. of Frankfurt, 1978.
[17] F. Stummel, Rounding errors in numerical solutions of two linear equations in two unknowns, Math. Methods Appl. Sci. 4 (1982), no. 4, 549 – 571. · Zbl 0505.65011
[18] F. Stummel, Rounding error analysis of elementary numerical algorithms, Fundamentals of numerical computation (computer-oriented numerical analysis) (Proc. Conf., Tech. Univ. Berlin, Berlin, 1979) Comput. Suppl., vol. 2, Springer, Vienna, 1980, pp. 169 – 195. · Zbl 0432.65023
[19] F. Stummel, ”Rounding error anlaysis of difference and extrapolation schemes.” (To appear.)
[20] Friedrich Stummel, Rounding error in Gaussian elimination of tridiagonal linear systems. Survey of results, Interval mathematics, 1980 (Freiburg, 1980) Academic Press, New York-London, 1980, pp. 223 – 245. · Zbl 0543.65011
[21] F. Stummel, ”Rounding error in Gaussian elimination of tridiagonal linear systems. I,” SIAM J. Numer. Anal. (Submitted.)
[22] F. Stummel, ”Rounding error in Gaussian elimination of tridiagonal linear systems. II,” Linear Algebra Appl. (Submitted.)
[23] F. Stummel, ”Forward error analysis of Gaussian elimination.” (To appear.)
[24] Martti Tienari, On some topological properties of numerical algorithms, Nordisk Tidskr. Informationsbehandling (BIT) 12 (1972), 409 – 433. · Zbl 0246.65018
[25] J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. · Zbl 1041.65502
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