\"The blocked orthogonalization algorithm for nonlinear regression developed in this work results from a study of matching problems having certain identifiable characteristics with algorithms which exploit those characteristics. The new algorithm represents an extension of an earlier algorithm by D. S. Grey using a blocked orthogonalization technique proposed by R. E. von Holdt. The result is a generalization of the Grey and the Gauss-Hartley algorithms which maintains the desirable properties of these algorithms while avoiding their more serious limitations. The new algorithm was found to be quite effective for solving problems in which the parameters in the model under consideration were \"naturally\" grouped.
Numerous criteria for evaluating algorithm performance are used to compare results of the new algorithm with those of the Davidon-Fletcher-Powell, Levenberg-Marquardt, Gauss Hartley, and Grey algorithms. Acceleration of the new algorithm using Cornwell's Linear Acceleration Technique is also studied. Zangwill's convergence theory establishes validity of the new algorithm for the nonquadratic case while numerical examples exhibit its robustness\"-- Abstract, p. ii
","abstract_html":"<p>"The blocked orthogonalization algorithm for nonlinear regression developed in this work results from a study of matching problems having certain identifiable characteristics with algorithms which exploit those characteristics. The new algorithm represents an extension of an earlier algorithm by D. S. Grey using a blocked orthogonalization technique proposed by R. E. von Holdt. The result is a generalization of the Grey and the Gauss-Hartley algorithms which maintains the desirable properties of these algorithms while avoiding their more serious limitations. The new algorithm was found to be quite effective for solving problems in which the parameters in the model under consideration were "naturally" grouped.</p> <p>Numerous criteria for evaluating algorithm performance are used to compare results of the new algorithm with those of the Davidon-Fletcher-Powell, Levenberg-Marquardt, Gauss Hartley, and Grey algorithms. Acceleration of the new algorithm using Cornwell's Linear Acceleration Technique is also studied. Zangwill's convergence theory establishes validity of the new algorithm for the nonquadratic case while numerical examples exhibit its robustness"-- Abstract, p. ii</p>","abstract_has_math":false,"creators":["St. Clair, Daniel C."],"institution":"University of Missouri--Rolla","degree_name":"Ph. D. in Mathematics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:18:43Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/259","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["St. Clair, Daniel C."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Mathematics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Rolla"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/259"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"The blocked orthogonalization algorithm for nonlinear regression developed in this work results from a study of matching problems having certain identifiable characteristics with algorithms which exploit those characteristics. The new algorithm represents an extension of an earlier algorithm by D. S. Grey using a blocked orthogonalization technique proposed by R. E. von Holdt. The result is a generalization of the Grey and the Gauss-Hartley algorithms which maintains the desirable properties of these algorithms while avoiding their more serious limitations. The new algorithm was found to be quite effective for solving problems in which the parameters in the model under consideration were \"naturally\" grouped.
Numerous criteria for evaluating algorithm performance are used to compare results of the new algorithm with those of the Davidon-Fletcher-Powell, Levenberg-Marquardt, Gauss Hartley, and Grey algorithms. Acceleration of the new algorithm using Cornwell's Linear Acceleration Technique is also studied. Zangwill's convergence theory establishes validity of the new algorithm for the nonquadratic case while numerical examples exhibit its robustness\"-- Abstract, p. ii
"]},{"key":"dc:title","label":"Title","values":["A blocked orthogonalization method for nonlinear regression"]}]}],"canonical_facts":{"dc:creator":["St. Clair, Daniel C."],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["\"The blocked orthogonalization algorithm for nonlinear regression developed in this work results from a study of matching problems having certain identifiable characteristics with algorithms which exploit those characteristics. The new algorithm represents an extension of an earlier algorithm by D. S. Grey using a blocked orthogonalization technique proposed by R. E. von Holdt. The result is a generalization of the Grey and the Gauss-Hartley algorithms which maintains the desirable properties of these algorithms while avoiding their more serious limitations. The new algorithm was found to be quite effective for solving problems in which the parameters in the model under consideration were \"naturally\" grouped.
Numerous criteria for evaluating algorithm performance are used to compare results of the new algorithm with those of the Davidon-Fletcher-Powell, Levenberg-Marquardt, Gauss Hartley, and Grey algorithms. Acceleration of the new algorithm using Cornwell's Linear Acceleration Technique is also studied. Zangwill's convergence theory establishes validity of the new algorithm for the nonquadratic case while numerical examples exhibit its robustness\"-- Abstract, p. ii
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