Pseudosolution of Linear Functional Equations

Parameters Estimation of Linear Functional Relationships

Alexander S. Mechenov (Autor)

Buch | Softcover

238 Seiten

2005
Springer-Verlag New York Inc.
978-0-387-24505-8 (ISBN)

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In the book there are introduced models and methods of construction of pseudo-solutions for the well-posed and ill-posed linear functional equations circumscribing models passive, active and complicated experiments. Two types of the functional equations are considered: systems of the linear algebraic equations and linear integral equations. Methods of construction of pseudos6lutions are developed in the presence of passive right-hand side errors for two types of operator errors: passive measurements and active representation errors of the operator, and all their combinations. For the determined and stochastic models of passive experiments the method of the least distances of construction of pseudosolutions is created, the maximum likelihood method of construction of pseudosolutions is applied for active experiments, and then methods for combinations of models of regression, of passive and of active experiments are created. We have constructed regularized variants of these methods for systems of the linear algebraic equations with the degenerated matrices and for linear integral equations of the first kind. In pure mathematics, the solution techniques of the functional equations with exact input data more often are studied. In applied mathematics, problem consists in construction of pseudosolutions, that is, solution of the hctional equations with perturbed input data. Such problem in many cases is incomparably more complicated. The book is devoted to a problem of construction of a pseudosolution (the problem of a parameter estimation) in the following fundamental sections of applied mathematics: confluent models passive, active and the every possible mixed experiments.

Contents.- General Preface.- Labels and Abbreviations.- Chapter I. Systems of Linear Algebraic Equations.- Chapter II. Systems of Linear Algebraic Equations.- Chapter III. Linear Integral Equations.- References.- Application.- Index.- Glossary of Symbols.

Reihe/Serie	Mathematics and Its Applications ; 576
Reihe/Serie	Mathematics and Its Applications ; 576
Zusatzinfo	X, 238 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Wirtschaft ► Volkswirtschaftslehre ► Ökonometrie
ISBN-10	0-387-24505-7 / 0387245057
ISBN-13	978-0-387-24505-8 / 9780387245058
Zustand	Neuware