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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.


The probability that a slightly perturbed numerical analysis problem is difficult
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by Peter Bürgisser, Felipe Cucker and Martin Lotz PDF
Math. Comp. 77 (2008), 1559-1583 Request permission


We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric invariants of the corresponding sets of ill-posed inputs. Several applications to linear and polynomial equation solving show that the estimates obtained in this way are easy to derive and quite accurate. The main theorem is based on a volume estimate of $\varepsilon$-tubular neighborhoods around a real algebraic subvariety of a sphere, intersected with a spherical disk of radius $\sigma$. Besides $\varepsilon$ and $\sigma$, this bound depends only on the dimension of the sphere and on the degree of the defining equations.
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Additional Information
  • Peter Bürgisser
  • Affiliation: Department of Mathematics, University of Paderborn, Germany
  • MR Author ID: 316251
  • Email:
  • Felipe Cucker
  • Affiliation: Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong
  • Email:
  • Martin Lotz
  • Affiliation: Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong
  • Email:
  • Received by editor(s): September 28, 2006
  • Received by editor(s) in revised form: April 23, 2007
  • Published electronically: January 30, 2008
  • Additional Notes: Part of these results were announced in C.R. Acad. Sci. Paris, Ser. I 343 (2006) 145–150.
    The first author was partially supported by DFG grant BU 1371.
    The second and third authors were partially supported by CityU SRG grant 7001860.
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 77 (2008), 1559-1583
  • MSC (2000): Primary 65Y20; Secondary 65F35, 65H20
  • DOI:
  • MathSciNet review: 2398780