Introduction to Numerical Analysis

By F. B. Hildebrand. 1976

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Citations in the corpus

On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions (2015, methodology): “ture is another class of methods for one-dimensional integrals: it is based on a basis of orthogonal polynomials for L2(dρ) where dρis a probability measure supported in an interval, and their zeros (Hildebrand, 1987, Chap. 8). This leads to quadrature rules which are exact for polynomials of degree”
Analytically pricing European-style options under the modified Black-Scholes equation with a spatial-fractional derivative (2014, unknown): “The detailed implementation of this scheme can be found in many textbooks regrading numerical methods [9] and is thus omitted here.”
Sigma-point kalman filters for probabilistic inference in dynamic state-space models (2004, methodology): “Further insight into the sigma-point approach can be gained by relating it to a numerical integral evaluation technique called Gaussian quadrature [79, 156] utilizing the GaussHermite rule: In the scalar case, the Gauss-Hermite rule is given by ∫ ∞ −∞ f(x) 1 √ 2π e−x 2 dx = m ∑”
Image Analysis by Tchebichef Moments (2001, background): “The discrete Tchebichef polynomials [3], [8] are defined as”
On the Performance of Non-orthogonal Multiple Access Systems With Partial Channel Information (2016, methodology): “Substributing (60) into (59), and using Gauss-Chebyshev integration [20] again, we can obtain the final result of Q1 as follows:”
Akaike-type criteria and the reliability of inference: Model selection versus statistical model specification (2010, background): “For =100 () ' 66 the expected number of runs in the residuals should be considerably higher than (+2), otherwise they are likely to exhibit Markov dependence; see Spanos (1999).”
A differential scheme for elastic properties of rocks with dry or saturated cracks (2002, methodology): “We use two Runge–Kutta schemes from Hildebrand (1956): eqs (6.13.15) and (6.14.5).”