A Theoretical Introduction to Numerical Analysis

By V. Ryaben'kii, S. Tsynkov. 2006

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Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next (2022, methodology): “When solving differential equations using a numerical discretization technique, we are interested in the numerical method’s stability, consistency, and convergence [8, 150, 171].”
Distributed Non-Convex First-Order optimization and Information Processing: Lower Complexity Bounds and Rate Optimal Algorithms (2018, methodology): “In particular, to achieve constant reduction the total number of required Chebyshev iteration is proportional to √ 1/ξ(R), rather than 1/ξ(R) in conventional iterative scheme such as the Richardson’s iteration [46].”
The Matrix Exponential (2015, unknown): “A wellknown method to compute ym(t) ≈ exp(−tA)v is based on the Chebyshev polynomial expansion (see for instance [26, 22]):”
Encrypted Accelerated Least Squares Regression (2017, background): “= (λmax − λmin)/(λmax + λmin), where λmax and λmin denote the largest and smallest eigenvalues of XTX, respectively (see Ryaben’kii and Tsynkov, 2006, Theorem 6.3 for all proofs).”