Abstract
The boundary layer of a finite domain [a, b] covers mesoscopic lateral neighborhoods, inside [a, b], of the endpoints a and b. The correct diagnostic of the integrand behavior at a and b, based on its sampling inside the boundary layer, is the first from a set of hierarchically ordered criteria allowing a priori Bayesian inference on efficient mesh generation in automatic adaptive quadrature.
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References
R. Piessens, E. deDoncker-Kapenga, C. W. Überhuber, and D. K. Kahaner, QUADPACK, a Subroutine Package for Automatic Integration (Springer, Berlin, 1983).
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed. (Academic, Orlando, USA, 1984).
A. R. Krommer and C. W. Ueberhuber, Computational Integration (SIAM, Philadelphia, 1998).
N. M. Plakida, High-Temperature Superconductivity: Experiment and Theory (Springer, Berlin, 1995).
Gh. Adam and S. Adam, Comput. Phys. Commun. 135, 261 (2001).
Gh. Adam, S. Adam, and N. M. Plakida, Comput. Phys. Commun. 154, 49 (2003).
Gh. Adam and S. Adam, in Proc. of ICCAM2004 Conf., July 25–31, 2004 (Univ. Leuven, Belgium, 2004).
E. T. Jaynes, “Bayesian Methods: An Introductory Tutorial,” in Maximum Entropy and Bayesian Methods in Applied Statistics, Ed. by J. H. Justice (Cambridge Univ., Cambridge, 1986).
Gh. Adam, S. Adam, A. Tifrea, and A. Neacsu, Romanian Rep. Phys. 58, 107 (2006).
D. Goldberg, “What Every Computer Scientist Should Know about Floating-Point Arithmetic,” Computing Surv. (March, 1991), http://www.validlab.com/goldberg/paper.pdf.
W. Kahan, “Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic” (May, 1996), http://www.cs.berkeley.edu/:_wkahan/ieee754status/ieee754.ps.
W. Kahan, “How Futile are Mindless Assessments of Roundoff in Floating-Point Computation” (in progress), http://www.cs.berkeley.edu/:_wkahan/Mindless.pdf.
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The text was submitted by the authors in English.