A forward-only Lanczos gradient approximation for Hermitian matrix function bilinear forms whose error scales with the same residual norm as the forward approximation and appears stable without reorthogonalization.
Efficient solution of parabolic equations by Krylov approximation methods.SIAM Journal on Scientific and Statistical Computing, 13(5):1236– 1264, 1992
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Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions
A forward-only Lanczos gradient approximation for Hermitian matrix function bilinear forms whose error scales with the same residual norm as the forward approximation and appears stable without reorthogonalization.