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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On Gauss’ speeding up device in the theory of single step iteration.
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by Alexander M. Ostrowski PDF
Math. Comp. 12 (1958), 116-132 Request permission

Corrigendum: Math. Comp. 13 (1959), 335.
References
    R. Dedekind, “Gauss in seiner Vorlesung über die Methode der kleinsten Quadrate,” Festschrift zur Feier des 150-jährigen Bestehens der königlichen Gesellschaft der Wissenschaften zu Göttingen. Berlin, 1901, p. 45-49. R. Dedekind, Gesammelte mathematische Werke. Herausgegeben von R. Fricke, E. Noether, & Ö. Ore. Bd. II. 1931, Braunschweig, p. 293-306, especially p. 300-301.
  • George E. Forsythe and Theodore S. Motzkin, An extension of Gauss’ transformation for improving the condition of systems of linear equations, Math. Tables Aids Comput. 6 (1952), 9–17. MR 48162, DOI 10.1090/S0025-5718-1952-0048162-0
    • C. F. Gauss, “Letter to Gerling,” 26 December 1823, Werke, v. 9, p. 278-281. For an annotated translation of Gauss’ letter by G. E. Forsythe, see MTAC, v. 5, 1951, p. 255-258.
  • Werner Gautschi, The asymptotic behaviour of powers of matrices, Duke Math. J. 20 (1953), 127–140. MR 56568
    • Christian Ludwig Gerling, Die Ausgleichsrechnung der practischen Geometrie. Hamburg and Gotha, 1843. F. R. Helmert, Die Ausgleichsrechnung nach der Methode der kleinsten Quadrate, mit Anwendung auf die Geodäsie und die Theorie der Messinstrumente, Leipzig, 1872, p. 136.
  • A. M. Ostrowski, Two explicit formulae for the distribution function of the sums of $n$ uniformly distributed independent variables, Arch. Math. (Basel) 3 (1952), 451–459. MR 56222, DOI 10.1007/BF01900561
  • A. M. Ostrowski, On the linear iteration procedures for symmetric matrices, Rend. Mat. e Appl. (5) 14 (1954), 140–163. MR 70261
  • Alexander Ostrowski, Über Normen von Matrizen, Math. Z. 63 (1955), 2–18 (German). MR 72100, DOI 10.1007/BF01187920
  • Edgar Reich, On the convergence of the classical iterative method of solving linear simultaneous equations, Ann. Math. Statistics 20 (1949), 448–451. MR 31327, DOI 10.1214/aoms/1177729998
    • W. Schmeidler, Vorträge über Determinanten und Matrizen mit Anwendungen in Physik und Technik, Berlin, 1949. Ludwig Seidel, “Über ein Verfahren, die Gleichungen, auf welche die Methode der kleinsten Quadrate führt, sowie lineare Gleichungen überhaupt, durch successive Annäherung aufzulösen,” Akad. Wiss., Munich, Mathematisch-Naturwissenschaftliche Abteilung, v. 11, No. 3, 1874, p. 81-108. R. V. Southwell, “Stress-calculation in frameworks by the method of systematic relaxation of constraints,” I & II, Roy. Soc. London, Proc., A 151, 1935, p. 56-95.
  • Rudolf Zurmühl, Matrizen. Eine Darstellung für Ingenieure, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1950 (German). MR 0036212
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Additional Information
  • © Copyright 1958 American Mathematical Society
  • Journal: Math. Comp. 12 (1958), 116-132
  • MSC: Primary 65.00
  • DOI: https://doi.org/10.1090/S0025-5718-1958-0099747-2
  • MathSciNet review: 0099747