A deflated version of the Conjugate Gradient Algorithm

J. Erhel, F. Guyomarc'h, Y. Saad and M. Yeung

Department of Computer Science and Engineering, University of Minnesota


We present a deflated version of the conjugate gradient algorithm for solving linear systems. The new algorithm can be useful in cases when there are a small number of eigenvalues of the iteration matrix which are very close to the origin. It can also be useful when solving linear systems with multiple right-hand sides, since the eigenvalue information gathered from solving one linear system can be recycled for solving the next systems and then updated.