Incomplete alternating projection method for large inconsistent linear systems Original Research Article

We consider in the paper the problem of finding an approximat solution of a large scale inconsistent linear system Ainverted perpendicularx=b, where A is an n×m real matrix and image. The problem is a special case of the following problem. Let image be nonempty and affine subspaces; find an element of the intersection image or find points image and image which realize the distance between these two subspaces. Problems of this kind appear in many applications, e.g. in the image reconstruction or in the intensity modulated radiation therapy (see, e.g. [Y. Censor, S.A. Zenios, Parallel Optimization, Theory, Algorithms and Applications, Oxford University Press, New York, 1997; H. Stark, Y. Yang, Vector Space Projections. A Numerical Approach to Signal and Image Processing, Neural Nets and Optics, John Wiley & Sons, Inc., New York, 1998; H.W. Hamacher, K.-H. Küfer, Inverse radiation therapy planning – a multiple objective optimization approach, Discrete Appl. Math. 118 (2002) 145–161]).