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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Pseudosolution of Linear Functional Equations - Parameters Estimation of Linear Functional Relationships (Paperback, 2005 ed.)
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Pseudosolution of Linear Functional Equations - Parameters Estimation of Linear Functional Relationships (Paperback, 2005 ed.)
Series: Mathematics and Its Applications, 576
Expected to ship within 10 - 15 working days
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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.
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