Accelerated Methods for the Block Cimmino Row Projection Method for Solving Large Nonsymmetric Linear Systems
نویسنده
چکیده
The use of the row block projection method (block Cimmino) for solving nonsymmetric linear system Ax = b gives rise to a symmetric positive definite system G x = g, where B is the sum of orthogonal projection matrices Pi = Ai(ATAi)-'AT, and where the Ar's are block rows of A. In this paper we present an efficient implementation of the cgT method for solving the derived symmetric positive definite system. We use initial smoothing to accelerate the method and we derive efficient techniques for estimating the initial smoothed vector. Numerical results are given for the 2 row block case and since the eigenvalues of G can then be calculated, we by-pass the computation of orthogonal projections Pix of a vector x ont0 the range of Ai by solving a transformed equivalent system. Test results show that the method is robust.
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