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Least squares methods for Volterra equations and generalizations
Author(s) -
Bedivan Dana M.,
Fix George J.
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.10501
Subject(s) - mathematics , quadrature (astronomy) , volterra integral equation , least squares function approximation , partial derivative , convergence (economics) , non linear least squares , convolution (computer science) , gauss–kronrod quadrature formula , calculus (dental) , mathematical analysis , integral equation , nyström method , explained sum of squares , statistics , computer science , medicine , engineering , dentistry , estimator , machine learning , economic growth , artificial neural network , electrical engineering , economics
In this article least squares approximations to Volterra integral equations are considered, both with exact integration and with quadrature. Optimal error estimates are derived, and it is shown that the same order of convergence is obtained in both cases with only modest requirements on the quadrature rule used in the latter. The most important practical setting for least squares is the case of convolution kernels, and these are also studied in this article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 679–693, 1998