03059nam 2200445 450 99646656350331620210315184504.03-030-63343-810.1007/978-3-030-63343-1(CKB)4100000011763140(DE-He213)978-3-030-63343-1(MiAaPQ)EBC6478925(PPN)253859093(EXLCZ)99410000001176314020210315d2021 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierAn introduction to the mathematical theory of inverse problems /Andreas KirschThird edition.Cham, Switzerland :Springer,2021.1 online resource (XVII, 400 p. 13 illus.) Applied Mathematical Sciences ;Volume 1203-030-63342-X Introduction and Basic Concepts -- Regularization Theory for Equations of the First Kind -- Regularization by Discretization -- Nonlinear Inverse Problems -- Inverse Eigenvalue Problems -- An Inverse Problem in Electrical Impedance Tomography -- An Inverse Scattering Problem -- Basic Facts from Functional Analysis -- References -- Index.This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published. .Applied mathematical sciences (Springer-Verlag New York Inc.) ;Volume 120.Inverse problems (Differential equations)Inverse problems (Differential equations)515.357Kirsch Andreas1953-28299MiAaPQMiAaPQMiAaPQBOOK996466563503316Introduction to the mathematical theory of inverse problems349256UNISA01476nas 2200529-a 450 99620980470331620230227213019.01474-0028(OCoLC)45433441(CKB)954925499113(CONSER)--2007233728(MiAaPQ)37451(DE-599)ZDB2025432-5(EXLCZ)9995492549911320001128a19859999 s-- aengurmnu||||||||txtrdacontentcrdamediacrrdacarrierEconomics and philosophy[Cambridge, England] Cambridge University PressRefereed/Peer-reviewed0266-2671 Economics & philosophyECONOMICS & PHILOSOPHYECON PHILOSECON. PHILOSEconomicsPeriodicalsPhilosophyPeriodicalsEconomicsfast(OCoLC)fst00902116Philosophyfast(OCoLC)fst01060777WirtschaftsphilosophiegndAufsatzsammlunggndPeriodicals.fastEconomicsSerialsEconomicsPhilosophyEconomics.Philosophy.WirtschaftsphilosophieAufsatzsammlung330JOURNAL996209804703316Economics and philosophy798008UNISA