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Volume 22 - April 1981

Contents

Page 3 of 3

Front matter

  • ANZ volume 22 issue 3 Cover and Front matter

  • Published online by Cambridge University Press:
    17 February 2009, pp. f1-f2
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  • ANZ volume 22 issue 1 Cover and Front matter

  • Published online by Cambridge University Press:
    17 February 2009, pp. f1-f3
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Corrigendum

  • Solution of a general homogeneous linear difference equation†

  • V. N. Singh
  • Published online by Cambridge University Press:
    17 February 2009, p. 254
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  • In Section 3, since relation (6) is valid only for n ≥ 2r, the condition n ≥ r in relation (9) should be replaced by n ≥ 2r. When r ≤ n ≤ 2r − 1, relation (9) still holds but now relations (6) and (7) should be replaced, respectively, by the relations

    and

    the asterisk again denoting omission of the last column. The proof of (9) for r ≤ n ≤ 2r − 1 is exactly similar to its proof for n ≥ 2r.

Research Article

  • The extension of generalized cross-validation to a multi-parameter class of estimators

  • D. M. O'Brien, J. N. Holt
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    17 February 2009, pp. 501-514
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  • The method of generalized cross-validation (GCV) provides a good value for the “ridge” regularization parameter for an ill-conditioned linear system, such as the system produced by discretization of a Fredholm integral equation of the first kind. In this note we apply GCV to a wider class of estimators than the one parameter ridge estimators. We observe that the expected values of the parameter mean-square error, the predictive mean-square error, and the GCV function are simultaneously minimized over this new class, so we accept the minimizer of the GCV function as the best computable estimator. We present a simple algorithm for computing this estimator from the data, so that a numerical search is not needed.

Back matter

  • ANZ volume 22 issue 1 Cover and Back matter

  • Published online by Cambridge University Press:
    17 February 2009, pp. b1-b2
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Research Article

  • Stability analysis of Runge–Kutta methods applied to a basic Volterra integral equation

  • Christopher T. H. Baker, Joan C. Wilkinson
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    17 February 2009, pp. 515-538
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  • Our purpose in this paper is to display the stability analysis of Runge–Kutta methods applied to a Volterra integral equation of a simple form. As prerequisite we define, and then develop the structure of, the class of Runge–Kutta methods considered. The test equation is taken as the “;basic” equation ; the simple form of this equation permits ready insight into features which are more obscure when considering (as elsewhere [1], [2], [6]) equations of a more complicated form. Due to the structure of the methods and the nature of the test equation, the stability analysis reduces to the study of recurrence relations of the form Фk + 1 = MФ k + γk (k = 0, 1, 2, …) which are common in stability discussions in numerical analysis.

Back matter

  • ANZ volume 22 issue 3 Cover and Back matter

  • Published online by Cambridge University Press:
    17 February 2009, pp. b1-b2
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Front matter

  • ANZ volume 22 issue 2 Cover and Front matter

  • Published online by Cambridge University Press:
    17 February 2009, pp. f1-f2
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Research Article

  • A convergence theorem for singular integral equations

  • David Elliott
  • Published online by Cambridge University Press:
    17 February 2009, pp. 539-552
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  • The principal result of this paper states sufficient conditions for the convergence of the solutions of certain linear algebraic equations to the solution of a (linear) singular integral equation with Cauchy kernel. The motivation for this study has been the need to provide a convergence theory for a collocation method applied to the singular integral equation taken over the arc (−1, 1). However, much of the analysis will be applicable both to other approximation methods and to singular integral equations taken over other arcs or contours. An estimate for the rate of convergence is also given.

Back matter

  • ANZ volume 22 issue 2 Cover and Back matter

  • Published online by Cambridge University Press:
    17 February 2009, pp. b1-b2
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Index for Volume 22

  • Contents of Volume 22

  • Published online by Cambridge University Press:
    17 February 2009, pp. 553-554
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Front matter

  • ANZ volume 22 issue 4 Cover and Front matter

  • Published online by Cambridge University Press:
    17 February 2009, pp. f1-f3
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Back matter

  • ANZ volume 22 issue 4 Cover and Back matter

  • Published online by Cambridge University Press:
    17 February 2009, pp. b1-b2
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Page 3 of 3