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A Complete Resolution of Forsythe's Conjecture for Restarted Conjugate Gradients
Matthew J. Colbrook, George Stepaniants, Alex Townsend
Forsythe's conjecture, published in 1968, asserts that for each restart length , every exact-arithmetic restarted conjugate-gradient iteration on a real symmetric positive defin…
A Proof of the Forsythe Conjecture for the Two-Step Restarted Conjugate Gradient Method
Matthew J. Colbrook, George Stepaniants, Alex Townsend
Forsythe conjectured in 1968 that the normalized residual directions of restarted conjugate gradients approach a two-cycle. We prove the conjecture for restart length two: unless t…
Learning Memory and Material Dependent Constitutive Laws
Kaushik Bhattacharya, Lianghao Cao, George Stepaniants +2
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale…