Discrepancy principle for DSM II

✍ Scribed by A.G. Ramm

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 160 KB
• Volume: 13
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2006.11.006

✦ Synopsis

Let Ay = f, A is a linear operator in a Hilbert space H, y ? N(A) :¼ {u :

Given f d , one wants to construct u d such that lim d!0 ku d À yk = 0. Two versions of discrepancy principles for the DSM (dynamical systems method) for finding the stopping time and calculating the stable solution u d to the original equation Ay = f are formulated and mathematically justified.