Details

Pseudosolution of Linear Functional Equations


Pseudosolution of Linear Functional Equations

Parameters Estimation of Linear Functional Relationships
Mathematics and Its Applications, Band 576

von: Alexander S. Mechenov

53,49 €

Verlag: Springer
Format: PDF
Veröffentl.: 25.07.2005
ISBN/EAN: 9780387245065
Sprache: englisch
Anzahl Seiten: 238

Dieses eBook enthält ein Wasserzeichen.

Beschreibungen

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.
<P>
<P></P>This book presents the author’s new method of two-stage maximization of likelihood function, which helps to solve a series of non-solving before the well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations (or, in statistical terminology, parameters’ estimators of functional relationships) and linear integral equations in the presence of deterministic and random errors in the initial data. This book, for the first time, presents a solution of the problem of reciprocal influence of passive errors of regressors and of active errors of predictors by computing point estimators of functional relationships.
<P><EM>Audience</EM></P>
<P>This book is intended for students, postgraduate students, scientists, and other researchers on handling economical and technical data. The book is especially intended for those who constantly use regression analysis in their own research and for those who create the mathematical software for computers. </P>
Presents for the first time a solution of the problem of reciprocal influence of passive errors of regressors and of active errors of predictors by computing point estimators of functional relationships

Diese Produkte könnten Sie auch interessieren:

Modeling Uncertainty
Modeling Uncertainty
von: Moshe Dror, Pierre L'Ecuyer, Ferenc Szidarovszky
PDF ebook
236,81 €
Level Crossing Methods in Stochastic Models
Level Crossing Methods in Stochastic Models
von: Percy H. Brill
PDF ebook
203,29 €
Continuous Bivariate Distributions
Continuous Bivariate Distributions
von: N. Balakrishnan, Chin Diew Lai
PDF ebook
128,39 €