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A deflated restarted Lanczos algorithm is given for both solving symmetriclinear equations and computing eigenvalues and eigenvectors. The restartinglimits the storage so that finding eigenvectors is practical. Meanwhile, thedeflating from the presence of the eigenvectors allows the linear equations togenerally have good convergence in spite of the restarting. Somereorthogonalization is necessary to control roundoff error, and severalapproaches are discussed. The eigenvectors generated while solving the linearequations can be used to help solve systems with multiple right-hand sides.Experiments are given with large matrices from quantum chromodynamics that havemany right-hand sides.

Deflated and restarted symmetric Lanczos methods for eigenvalues and linear equations with multiple right-hand sides