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4 results

  • Existence and uniqueness regions for solutions of nonlinear equations

  • A.L. Andrew
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 19 / Issue 2 / October 1978
    Published online by Cambridge University Press:
    17 April 2009, pp. 277-282
    Print publication:
    October 1978
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  • A refinement of the Newton-Kantorovich Theorem, which has many-potential applications in existence - uniqueness theory, is used to strengthen a result of Lancaster and Rokne concerning existence and uniqueness regions for zeros of operator polynomials.

  • Error bounds for the modified Newton's method

  • A.L. Andrew
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 14 / Issue 3 / June 1976
    Published online by Cambridge University Press:
    17 April 2009, pp. 427-433
    Print publication:
    June 1976
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  • A strengthened form of the Kantorovich convergence theorem for the modified Newton's method is proved. The result is compared with previously known results.

  • Computation of eigenvectors corresponding to multiple eigenvalues

  • A.L. Andrew, G.C. Elton
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 4 / Issue 3 / June 1971
    Published online by Cambridge University Press:
    17 April 2009, pp. 419-422
    Print publication:
    June 1971
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  • This paper examines a class of common numerical methods for computing eigenvectors of a compact linear operator. A necessary and sufficient condition is established for every element of an arbitrary given eigenspace to be the limit of a sequence of the approximate eigenvectors obtained by any given method in this class.

  • Two Properties of Integers

  • A.L. Andrew
  • Journal:
    The Mathematical Gazette / Volume 48 / Issue 365 / October 1964
    Published online by Cambridge University Press:
    03 November 2016, pp. 285-287
    Print publication:
    October 1964

  • In a recent competition (see M.R. 23 (1962), A1482) it was required to show that the set {2, 3, 4} has the property, here called Pv that every number x in (0, 1] (i.e. 0 < x ≤ 1) can be expressed in the form , where m 1 is an integer and belongs to the set for all i.