A powerful iterative solver for system of equations has been developed. This solver, Generalized Vector Sampled Pattern Matching (GVSPM), enables us to obtain the solution of any ill-posed linear system equations, e.g., having rectangular or singular matrix. The key idea is that the objective function is the angle obtained by an inner product between the input vector and solution system of equations. This paper reviews the Generalized Sampled Pattern Matching (6 SPM) method, which is the original of proposed method, and then introduces the GVSPM method along with solution algorithm. The theoretical background and applications to inverse source problems on magnetic fields are described. From the applications, the GSPM and GVSPM methods tend to lead the discontinuous and continuous solutions, respectively. However, the GVSPM has the advantages of stability and convergence.
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