Pseudosolution of Linear Functional Equations: Parameters Estimation of Linear Functional Relationships

ISBN-13: 9780387245058 / Angielski / Miękka / 2005 / 238 str.

Alexander S. Mechenov

Opis

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.

Recenzje

From the reviews of the first edition:

"This book presents a method of two-stage maximization of a likelihood function, which helps to solve a series of non-solved before well-posed and ill-posed problems of pseudosolution computing systems of linear algebraic equations … . This book is intended for students, postgraduate students, scientists, and other researchers handling economical and technical data. It is especially intended for those who constantly use regression analysis in their own research and for those who create mathematical software for computers." (Yuehua Wu, Zentralblatt MATH, Vol. 1077, 2006)

Spis treści

Systems of Linear Algebraic Equations.- Systems of Linear Algebraic Equations.- Linear Integral Equations.

Blurb

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.

Audience

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.