The block least squares method for solving nonsymmetric linear systems with multiple right-hand sides. (English) Zbl 1096.65040

Summary: We present the block least squares method for solving nonsymmetric linear systems with multiple right-hand sides. This method is based on the block bidiagonalization. We first derive two algorithms by using two different convergence criteria. The first one is based on independently minimizing the 2-norm of each column of the residual matrix and the second approach is based on minimizing the Frobenius norm of residual matrix. We then give some properties of these new algorithms. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the efficiency of the new method.


65F20 Numerical solutions to overdetermined systems, pseudoinverses
65F10 Iterative numerical methods for linear systems


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