Introduction to Numerical Analysis

By Arnold Neumaier. 2001

6,718 citations recorded by the source corpus.

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

Elucidating the Design Space of Diffusion-Based Generative Models (2022, methodology): “Higher-order Runge–Kutta methods [49] scale more favorably but require multiple evaluations of D θ per step.”
Gotta Go Fast When Generating Data with Score-Based Models (2021, methodology): “Rather than using Improved Euler [Süli and Mayers, 2003] as in Lamba [2003] or a high-order stochastic Runge-Kutta method [Rößler, 2010] as in Rackauckas and Nie [2017b] (which did not work well in our preliminary attempts with the Julia package) we instead rely on the stochastic Improved Euler’s…”
Approximation of bayesian efficiency in experimental choice designs (2008, neutral): “Gaussian quadrature is the best-known method, see e.g. Stoer and Bulirsch (2002).”
On approximation of functions by exponential sums (2005, methodology): “Using the Euler–Maclaurin formula (see [6] or [14, pp.”
Nonlinear Dynamical System Identification from Uncertain and Indirect Measurements (2004, methodology): “Overviews of approaches for iterative solutions of nonlinear optimization problems are given in several textbooks [Gill et al., 1981; Stoer & Bulirsch, 1993; Press et al., 1997].”
On VIX futures in the rough Bergomi model (2017, background): “In addition, the trapezoidal rule (Atkinson 1989, Chapter 5) in step 4 yields an error of order O(h2T).”
On the continuous contact force models for soft materials in multibody dynamics (2011, methodology): “In the present work, the trapezoidal rule is chosen to obtain the solution of this integral, which can be written as [ 64 ]”
Nuclear physics from lattice QCD (2010, methodology): “10 The method is more generally referred to as Prony’s method [71] after Gaspard Riche de Prony who first constructed it in 1795 [72].”
A Cross-Layer (Layer 2 + 3) Handoff Management Protocol for Next-Generation Wireless Systems (2006, methodology): “(It takes only a few iterations to calculate d when the Bisection method [24] is used.”
Flow‐induced reconfiguration of buoyant and flexible aquatic vegetation (2011, background): “For streamlined postures, however, the blades bend significantly over a short distance close to the bed, producing curvature that is much larger than 1/l2.”