Computational functional analysis. (English) Zbl 0574.46001

Moore, Ramon E.

Ellis Horwood Series in Mathematics and Its Applications. Chichester: Ellis Horwood Limited; Chichester etc.: Halsted Press, a Division of John Wiley & Sons. 156 p. hbk: £15.00; pbk: £7.95; $ 10.35 (1985).

The aim of the book is to apply concepts and techniques of functional analysis to approximate solutions of operator equations (algebraic, linear, non-linear, differential, integral and others).
Chapters 1 to 12 contain introductory topics from functional analysis: linear spaces, topological and metric spaces, Banach and Hilbert spaces, linear functionals and operators, types of convergence, reproducing kernel Hilbert spaces, compact operators. The rest of the book is devoted to approximate methods of solving operator equations: Newton’s type methods, Galerkin’s method, interval methods, homotopy and continuation methods.
The book is clearly written, contains many worked numerical examples and can be used as an excellent text-book for one - or two - semester courses at the first year graduate level.

Reviewer: S.Cobzaş

MSC:

46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65J05	General theory of numerical analysis in abstract spaces
47A50	Equations and inequalities involving linear operators, with vector unknowns
46B03	Isomorphic theory (including renorming) of Banach spaces

Keywords:

approximate solutions of operator equations; topological and metric spaces; Banach and Hilbert spaces; linear functionals and operators; types of convergence; reproducing kernel Hilbert spaces; compact operators; Newton’s type methods; Galerkin’s method; interval methods; homotopy and continuation methods