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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 Lehmer’s method for finding the zeros of a polynomial
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by G. W. Stewart PDF
Math. Comp. 23 (1969), 829-835 Request permission

Corrigendum: Math. Comp. 25 (1971), 203.
Corrigendum: Math. Comp. 25 (1971), 203.

Abstract:

Lehmer’s method for finding a zero of a polynomial is a procedure for searching the complex plane in such a way that a zero is isolated in a sequence of disks of decreasing radii. In this paper modifications of the method that improve its stability are given. The convergence of the method and the use of the resulting approximate zero to deflate the polynomial are discussed.
References
  • Duane A. Adams, A stopping criterion for polynomial root finding, Comm. ACM 10 (1967), 655–658. MR 0240969, DOI 10.1145/363717.363775
  • B. W. Boehm, Review No. 14,748 of Adams’ “A stopping criterion for polynomial root finding,” Comput. Rev., v. 9, 1968, pp. 395–396.
  • A. Cohn, Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise, Math. Z. 14 (1922), no. 1, 110–148 (German). MR 1544543, DOI 10.1007/BF01215894
  • D. H. Lehmer, “A machine method for solving polynomial equations,” J. Assoc. Comput. Mach., v. 8, 1961, pp. 151–162. J. Schur, “Über algebraische Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen,” Z. Angew. Math. Mech., v. 1, 1920, pp. 307–311. G. W. Stewart III, Some Topics in Numerical Analysis, Oak Ridge National Laboratory Report ORNL-4303, Sept. 1968.
  • J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
  • J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
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Additional Information
  • © Copyright 1969 American Mathematical Society
  • Journal: Math. Comp. 23 (1969), 829-835
  • MSC: Primary 65.50
  • DOI: https://doi.org/10.1090/S0025-5718-1969-0266425-3
  • MathSciNet review: 0266425