Cargando…
Inverse and ill-posed problems : theory and applications /
The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background mate...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
De Gruyter,
2011.
|
| Colección: | Inverse and ill-posed problems series ;
v. 55. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Ma 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn772845127 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr |n|---||||| | ||
| 008 | 120116s2011 gw a ob 001 0 eng d | ||
| 040 | |a EBLCP |b eng |e pn |c EBLCP |d OCLCQ |d YDXCP |d N$T |d OCLCQ |d OCLCF |d DEBSZ |d OCLCQ |d E7B |d IDEBK |d DEBBG |d OCLCQ |d AGLDB |d AZK |d MOR |d PIFAG |d ZCU |d OCLCQ |d MERUC |d OCLCQ |d DEGRU |d VTS |d ICG |d OCLCQ |d TKN |d STF |d LEAUB |d DKC |d AU@ |d OCLCQ |d M8D |d UKAHL |d OCLCQ |d AJS |d OCLCO |d OCLCQ | ||
| 019 | |a 785776523 |a 961565169 |a 988458757 |a 988521453 |a 992037295 | ||
| 020 | |a 9783110224016 |q (electronic bk.) | ||
| 020 | |a 3110224011 |q (electronic bk.) | ||
| 020 | |a 3110224003 | ||
| 020 | |a 9783110224009 | ||
| 020 | |z 9783110224009 |q (alk. paper) | ||
| 029 | 1 | |a AU@ |b 000051449648 | |
| 029 | 1 | |a CHBIS |b 010396555 | |
| 029 | 1 | |a CHVBK |b 331228122 | |
| 029 | 1 | |a DEBBG |b BV042347712 | |
| 029 | 1 | |a DEBBG |b BV043075759 | |
| 029 | 1 | |a DEBBG |b BV044160830 | |
| 029 | 1 | |a DEBSZ |b 372904084 | |
| 029 | 1 | |a DEBSZ |b 397221568 | |
| 029 | 1 | |a DEBSZ |b 400456028 | |
| 029 | 1 | |a DEBSZ |b 421457511 | |
| 029 | 1 | |a DEBSZ |b 478279558 | |
| 029 | 1 | |a NZ1 |b 14973261 | |
| 035 | |a (OCoLC)772845127 |z (OCoLC)785776523 |z (OCoLC)961565169 |z (OCoLC)988458757 |z (OCoLC)988521453 |z (OCoLC)992037295 | ||
| 050 | 4 | |a QA378.5 |b .K33 2011eb | |
| 072 | 7 | |a MAT |x 007000 |2 bisacsh | |
| 082 | 0 | 4 | |a 515.357 |2 23 |
| 084 | |a 65-02 |a 65M32 |a 65N20 |a 65N21 |2 msc | ||
| 084 | |a SK 950 |2 rvk |0 (DE-625)rvk/143273: | ||
| 049 | |a UAMI | ||
| 100 | 1 | |a Kabanikhin, S. I. | |
| 245 | 1 | 0 | |a Inverse and ill-posed problems : |b theory and applications / |c Sergey I. Kabanikhin. |
| 260 | |a Berlin : |b De Gruyter, |c 2011. | ||
| 300 | |a 1 online resource (xv, 475 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file |2 rda | ||
| 490 | 1 | |a Inverse and ill-posed problems series ; |v 55 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; Denotations; 1 Basic concepts and examples; 1.1 On the definition of inverse and ill-posed problems; 1.2 Examples of inverse and ill-posed problems; 2 Ill-posed problems; 2.1 Well-posed and ill-posed problems; 2.2 On stability in different spaces; 2.3 Quasi-solution. The Ivanov theorems; 2.4 The Lavrentiev method; 2.5 The Tikhonov regularization method; 2.6 Gradient methods; 2.7 An estimate of the convergence rate with respect to the objective functional; 2.8 Conditional stability estimate and strong convergence of gradient methods applied to ill-posed problems. | |
| 505 | 8 | |a 2.9 The pseudoinverse and the singular value decomposition of an operator3 Ill-posed problems of linear algebra; 3.1 Generalization of the concept of a solution. Pseudo-solutions; 3.2 Regularization method; 3.3 Criteria for choosing the regularization parameter; 3.4 Iterative regularization algorithms; 3.5 Singular value decomposition; 3.6 The singular value decomposition algorithm and the Godunov method; 3.7 The square root method; 3.8 Exercises; 4 Integral equations; 4.1 Fredholm integral equations of the first kind; 4.2 Regularization of linear Volterra integral equations of the first kind. | |
| 505 | 8 | |a 4.3 Volterra operator equations with boundedly Lipschitz-continuous kernel4.4 Local well-posedness and uniqueness on the whole; 4.5 Well-posedness in a neighborhood of the exact solution; 4.6 Regularization of nonlinear operator equations of the first kind; 5 Integral geometry; 5.1 The Radon problem; 5.2 Reconstructing a function from its spherical means; 5.3 Determining a function of a single variable from the values of its integrals. The problem of moments; 5.4 Inverse kinematic problem of seismology; 6 Inverse spectral and scattering problems. | |
| 505 | 8 | |a 6.1 Direct Sturm-Liouville problem on a finite interval6.2 Inverse Sturm-Liouville problems on a finite interval; 6.3 The Gelfand-Levitan method on a finite interval; 6.4 Inverse scattering problems; 6.5 Inverse scattering problems in the time domain; 7 Linear problems for hyperbolic equations; 7.1 Reconstruction of a function from its spherical means; 7.2 The Cauchy problem for a hyperbolic equation with data on a time-like surface; 7.3 The inverse thermoacoustic problem; 7.4 Linearized multidimensional inverse problem for the wave equation; 8 Linear problems for parabolic equations. | |
| 505 | 8 | |a 8.1 On the formulation of inverse problems for parabolic equations and their relationship with the corresponding inverse problems for hyperbolic equations8.2 Inverse problem of heat conduction with reverse time (retrospective inverse problem); 8.3 Inverse boundary-value problems and extension problems; 8.4 Interior problems and problems of determining sources; 9 Linear problems for elliptic equations; 9.1 The uniqueness theorem and a conditional stability estimate on a plane. | |
| 500 | |a 9.2 Formulation of the initial boundary value problem for the Laplace equation in the form of an inverse problem. Reduction to an operator equation. | ||
| 520 | |a The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Inverse problems (Differential equations) | |
| 650 | 0 | |a Boundary value problems |x Improperly posed problems. | |
| 650 | 6 | |a Problèmes inverses (Équations différentielles) | |
| 650 | 6 | |a Problèmes aux limites |x Problèmes mal posés. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Boundary value problems |x Improperly posed problems. |2 fast |0 (OCoLC)fst00837126 | |
| 650 | 7 | |a Inverse problems (Differential equations) |2 fast |0 (OCoLC)fst00978098 | |
| 776 | 0 | 8 | |i Print version: |a Kabanikhin, S I. |t Inverse and Ill-posed Problems : Theory and Applications. |d Berlin : De Gruyter, ©2011 |z 9783110224009 |
| 830 | 0 | |a Inverse and ill-posed problems series ; |v v. 55. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430031 |z Texto completo |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH25309357 | ||
| 938 | |a De Gruyter |b DEGR |n 9783110224016 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL835416 | ||
| 938 | |a ebrary |b EBRY |n ebr10527901 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis28650952 | ||
| 938 | |a YBP Library Services |b YANK |n 7349039 | ||
| 994 | |a 92 |b IZTAP | ||