A stability estimate on the regularized solution of the backward heat equation
APPLIED MATHEMATICS AND COMPUTATION, cilt.135, ss.561-567, 2003 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 135
- Basım Tarihi: 2003
- Doi Numarası: 10.1016/s0096-3003(02)00069-3
- Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.561-567
- Anahtar Kelimeler: inverse problem, regularization, backward heat equation, ill-posed problems
- Atatürk Üniversitesi Adresli: Hayır
Özet
Inverse problems, where one looks for causes for observed or desired effects, are usually "ill-posed", i.e., their solution is not unique or unstable with respect to data perturbations. We derive a stability estimate for the regularized solution of the backward heat equation which is needed for stable solution of this ill-posed problem. For this purpose, we construct a regularizer for a certain minimization problem and, in conclusion, the stability of this minimization procedure. (C) 2002 Elsevier Science Inc. All rights reserved.