TY - JOUR
T1 - Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem
AU - Hon, Y. C.
AU - Takeuchi, Tomoya
PY - 2011
Y1 - 2011
N2 - In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to provide a stable solution when the measurement data contain noises. Numerical results indicate that the proposed method is stable, efficient, and accurate. © 2010 Springer Science+Business Media, LLC.
AB - In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel is adopt to provide a stable solution when the measurement data contain noises. Numerical results indicate that the proposed method is stable, efficient, and accurate. © 2010 Springer Science+Business Media, LLC.
KW - Inverse problem
KW - Reproducing Hilbert kernel
KW - Tikhonov regularization
UR - http://www.scopus.com/inward/record.url?scp=78651437405&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-78651437405&origin=recordpage
U2 - 10.1007/s10444-010-9148-1
DO - 10.1007/s10444-010-9148-1
M3 - RGC 21 - Publication in refereed journal
SN - 1019-7168
VL - 34
SP - 167
EP - 183
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
IS - 2
ER -