TY  - EJOU
AU  - Liu, Chein-Shan 

TI  - An Optimal Multi-Vector Iterative Algorithm in a Krylov Subspace for Solving the Ill-Posed Linear Inverse Problems
T2  - Computers, Materials \& Continua

PY  - 2013
VL  - 33
IS  - 2
SN  - 1546-2226

AB  - An optimal m-vector descent iterative algorithm in a Krylov subspace is developed, of which the m weighting parameters are optimized from a properly defined objective function to accelerate the convergence rate in solving an ill-posed linear problem. The optimal multi-vector iterative algorithm (OMVIA) is convergent fast and accurate, which is verified by numerical tests of several linear inverse problems, including the backward heat conduction problem, the heat source identification problem, the inverse Cauchy problem, and the external force recovery problem. Because the OMVIA has a good filtering effect, the numerical results recovered are quite smooth with small error, even under a large noise up to 10%.
KW  - Linear inverse problems
KW  -  Ill-posed linear equations system
KW  -  Optimal multi-vector iterative algorithm (OMVIA)
KW  -  Future cone
KW  -  Invariant-manifold
KW  -  Krylov subspace method

DO  - 10.3970/cmc.2013.033.175