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A review of least‐squares methods for solving partial differential equations
Author(s) -
Eason Ernest D.
Publication year - 1976
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620100505
Subject(s) - mathematics , least squares function approximation , generalized least squares , generality , eigenvalues and eigenvectors , matching (statistics) , non linear least squares , mathematical optimization , boundary value problem , linear least squares , total least squares , explained sum of squares , algorithm , mathematical analysis , statistics , singular value decomposition , psychology , physics , quantum mechanics , estimator , psychotherapist
Continuous (integral) and discrete (point‐matching) least‐squares methods are presented for linear and non‐linear problems in boundary‐value, eigenvalue, and initial‐value form. The history is traced, and important theoretical and practical results are summarized. A comprehensive sample of the literature is presented, indexed to show type of application, version of least squares used, and results of comparison studies. The advantages of least‐squares methods are discussed, including convenience in formulation and error evaluation, generality of mixed and local (finite element) versions, and performance that is competitive with other methods.