Open Access

ARTICLE

An Optimal Multi-Vector Iterative Algorithm in a Krylov Subspace for Solving the Ill-Posed Linear Inverse Problems

Chein-Shan Liu ¹
1 Department of Civil Engineering, National Taiwan University, Taipei, Taiwan. E-mail: liucs@ntu.edu.tw

Computers, Materials & Continua 2013, 33(2), 175-198. https://doi.org/10.3970/cmc.2013.033.175

Abstract

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%.

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Keywords

Linear inverse problems, Ill-posed linear equations system, Optimal multi-vector iterative algorithm (OMVIA), Future cone, Invariant-manifold, Krylov subspace method

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