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math.NA2022★ 5 cited
Randomized matrix-free quadrature: unified and uniform bounds for stochastic Lanczos quadrature and the kernel polynomial method
Tyler Chen, Thomas Trogdon, Shashanka Ubaru
We analyze randomized matrix-free quadrature algorithms for spectrum and spectral sum approximation. The algorithms studied include the kernel polynomial method and stochastic Lanc…
math.NA2022★ 8 cited
Growth factors of random butterfly matrices and the stability of avoiding pivoting
John Peca-Medlin, Thomas Trogdon
Random butterfly matrices were introduced by Parker in 1995 to remove the need for pivoting when using Gaussian elimination. The growing applications of butterfly matrices have oft…