The computation of step-sizes which guarantee convergence in unconstrained minimization by descent methods is considered. The use of a “control” or “range” function is highly attractive for this purpose because of...
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The computation of step-sizes which guarantee convergence in unconstrained minimization by descent methods is considered. The use of a “control” or “range” function is highly attractive for this purpose because of its simplicity. Since the Armijo-Goldstein test may fail prematurely due to numerical instability near the minimizer, we consider a range function based on gradient values alone as has been done forg convex in [8]. numerical algorithms are given for the computation of step-sizes whose behaviour under roundoff is shown to be benign in the sense of F. L. Bauer [5].
In this paper, a new algorithm for a cubic spline fit with equally spaced data points and given end conditions is described. It provides a new understanding of how a spline fit works and possesses the following comput...
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In this paper, a new algorithm for a cubic spline fit with equally spaced data points and given end conditions is described. It provides a new understanding of how a spline fit works and possesses the following computational advantages: 1) It can solve large size problems (virtually unlimited). 2) The accuracy can be realistically controlled based on the characteristics of data. 3) The computation time-is linearly proportional to the size of the problem. 4) It can handle a localized fit. 4) It can handle a localizd. The new algorithm is particularly suitable to be implemented in minicomputers for cutting surfaces by numerically controlled machines and for other applications.
This correspondence presents the remainder-quotient (RQ)-algorithm for the resolution of Boolean equations. If w = w ( xkl, xj2, … XkN) = 1 is the Boolean equation equivalent to the system whose solution is desired, ...
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The iterative methods by Ben-Israel and others for computing the Moore-Penrose inverse of a matrix are examined. Ill conditioned test matrices are inverted by the methods and some difficulties are found out. The itera...
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The iterative methods by Ben-Israel and others for computing the Moore-Penrose inverse of a matrix are examined. Ill conditioned test matrices are inverted by the methods and some difficulties are found out. The iterative methods do not seem superior to direct ones.
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