Language:   Search:   Contact
World of
Mathematics Database
»ZBMATH« MSC 2000
MSC 2010 Reviewer
Service Subscription
»ZBMATH«
ZBMATH Database | Advanced Search Print
Read more | Try MathML | Hide
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

ZBMATH Database Simple Search Advanced Search Command Search

Advanced Search

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0817.65041
Hào, Dinh Nho
(Dinh Nho Háo)
A mollification method for ill-posed problems. (English)
[J] Numer. Math. 68, No.4, 469-506 (1994). ISSN 0029-599X; ISSN 0945-3245/e

The author develops a general theory of mollification for approximate solution of ill-posed linear problems in Banach space. For a given family of subspaces on which the problem is well-posed the idea is to construct a corresponding family of mollification operators which map the problem into a well-posed problem on the subspace. This is accomplished by minimizing an appropriate functional.\par Error estimates and optimal or ``quasi-optimal'' parameter choice strategies are established and the method is applied to problems of numerical differentiation, parabolic equations reversed in time, Cauchy problems for the Laplace equation, and other problems. In addition, new Hölder type estimates are established for the backward heat equation and for certain non-characteristic Cauchy problems for parabolic equations.
[C.W.Groetsch (Cincinnati)]
MSC 2000:
*65J10 Equations with linear operators (numerical methods)
65J20 Improperly posed problems (numerical methods in abstract spaces)
47A50 Equations and inequalities involving linear operators
65D25 Numerical differentiation
35R35 Free boundary problems for PDE
65M30 Improperly posed problems (IVP of PDE, numerical methods)

Keywords: mollification method; regularization; quasi-optimal parameter choice strategies; error estimates; ill-posed linear problems; Banach space; numerical differentiation; parabolic equations; Cauchy problems; Laplace equation; backward heat equation

Cited in: Zbl 1082.47044 Zbl 1046.35010

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

Login Username: Password:

Highlights
Scientific prize winners of the ICM 2010
Overhang
Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Master Server

Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences
Published by Springer-Verlag | Webmaster