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Refined Nonlinear Gaussian Quadrature Filter
American Control Conference, 2019Gaussian filters have been widely used in various applications due to their simplicity and effectiveness. For nonlinear estimation problems, Gaussian filters are usually developed from numerical quadrature rules to approximate the Gaussian weighted ...
Bin Jia, M. Xin
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Padé approximation and gaussian quadrature
Bulletin of the Australian Mathematical Society, 1974For certain types of formal power series, including the series of Stieltjes, we prove that the [n, n+j], j ≥ −1, Padé approximants coincide with certain gaussian quadrature formulae and hence, convergence of these approximants follows immediately.
Allen, G. D. +4 more
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Gaussian quadrature rules with an exponential weight on the real semiaxis
, 2014We consider some “truncated” Gaussian rules based on the zeros of the orthonormal polynomials w.r.t. the weight function w(x) = e−x −α−xβ with x ∈ (0,+∞), α > 0 and β > 1.
G. Mastroianni +2 more
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Gaussian interval quadrature formula
Numerische Mathematik, 2001Let \(U_N=\{u_0,...,u_N\}, (V_N=\{1,v_1,...,v_N\})\) be a Chebyshev (Markov) system on the interval \([a,b],\) respectively. For a given set of ordered non-overlapping intervals \([c_k,d_k]\subseteq [a,b], k=1,...,n\) the authors consider the multiple node interval quadrature formula (with respect to \(V_N\)) \[ \int_a^b\mu(t)f(t)dt\approx \sum_{k=1}^n\
Bojanov, Borislav D., Petrov, Petar P.
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Theory and Applications of Gaussian Quadrature Methods
Theory and Applications of Gaussian Quadrature Methods, 2011Gaussian quadrature is a powerful technique for numerical integration that falls under the broad category of spectral methods. The purpose of this work is to provide an introduction to the theory and practice of Gaussian quadrature.
N. Kovvali
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Quarterly Journal of the Royal Meteorological Society, 2012
AbstractA new incremental four‐dimensional variational (4D‐Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with ...
R. J. J. Stappers, J. Barkmeijer
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AbstractA new incremental four‐dimensional variational (4D‐Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with ...
R. J. J. Stappers, J. Barkmeijer
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Concerning Gaussian–Chebyshev Quadrature Errors
SIAM Journal on Numerical Analysis, 1972We introduce a method for estimating errors in the Gaussian–Chebyshev quadrature formulas for functions of low order continuity. In particular, we improve an error bound obtained by Johnson and Riess.
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An improved morgenstern-price method using gaussian quadrature
Computers and geotechnics, 2022Weihang Ouyang, Si-Wei Liu, Yi Yang
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Gaussian-quadrature formulas for
Journal of Statistical Computation and Simulation, 1982(1982). Gaussian-quadrature formulas for. Journal of Statistical Computation and Simulation: Vol. 15, No. 2-3, pp. 155-160.
David Kahaner +2 more
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