Results 21 to 30 of about 678 (97)

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

, 1993
Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis ...
A Pringsheim, A Pringsheim, A Seiberg, AA Gonchar, AA Markov, AA Markov, AA Markov, AM Al-Rashed, AS Kronrod, AS Kronrod, B Baillaud, C Berg, C Brezinski, C Hermite, CL Siegel, D Hubert, D Hubert, D Hubert, DS Lubinsky, DV Chudnovsky, DV Chudnovsky, E Cosserat, E Hendriksen, EB Christoffel, EB Vleck Van, EB Vleck Van, EB Vleck Van, F Hausdorff, F Peherstorfer, FWJ Olver, G Darboux, G Darboux, G Freud, G Gasper, G Monegato, G Polya, G Szegö, G Szegö, G Szegő, G Vitali, G Vitali, GH Hardy, GH Hardy, H Bruns, H Hamburger, H Hamburger, H Hamburger, H Padé, H Padé, H Stahl, H Widom, H Widom, H Zaheer, HN Mhaskar, HS Wall, J Favard, JA Shohat, JA Shohat, JL Ullman, K Aomoto, K Possé, K Possé, L Carlitz, L Lorch, L Lorentzen, L Schur, LJ Rogers, LJ Rogers, M Alam, M Fekete, M Prévost, M Riesz, M Tsuji, MEH Ismail, MEH Ismail, MG Krein, MG Krein, MH Stone, ML Mehta, NI Akhiezer, NY Vilenkin, O Njåstad, O Perron, O Perron, P Erdős, P Montel, PG Nevai, PJ Forrester, PL Chebyshev, PL Pastro, R Askey, RA Gustafson, S Karlin, S Karlin, S Karlin, T Carleman, T Carleman, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TS Chihara, TS Chihara, TS Chihara, W Assche Van, W Gautschi, W Gautschi, W Gautschi, W Hahn, W Ledermann, WB Jones, WB Jones, WB Jones, YL Geronimus   +121 more
core   +2 more sources

Influence of Surface Energy Effects on Elastic Fields of a Layered Elastic Medium under Surface Loading

Advances in Materials Science and Engineering, Volume 2017, Issue 1, 2017., 2017
This paper presents the analysis of a layered elastic half space under the action of axisymmetric surface loading and the influence of the surface energy effects. The boundary value problems for the bulk and the surface are formulated based on classical linear elasticity and a complete Gurtin‐Murdoch constitutive relation. An analytical technique using
Supakorn Tirapat, Teerapong Senjuntichai, Jaroon Rungamornrat, Philip Eisenlohr   +3 more
wiley   +1 more source

A Short Review of FDTD‐Based Methods for Uncertainty Quantification in Computational Electromagnetics

Mathematical Problems in Engineering, Volume 2017, Issue 1, 2017., 2017
We provide a review of selected computational methodologies that are based on the deterministic finite‐difference time‐domain algorithm and are suitable for the investigation of electromagnetic problems involving uncertainties. As it will become apparent, several alternatives capable of performing uncertainty quantification in a variety of cases exist,
Theodoros T. Zygiridis, Antonios Tsourdos   +1 more
wiley   +1 more source

The Cosmic Linear Anisotropy Solving System (CLASS) IV: Efficient implementation of non-cold relics

, 2011
We present a new flexible, fast and accurate way to implement massive neutrinos, warm dark matter and any other non-cold dark matter relics in Boltzmann codes.
A. Lewis, D. Blas, D. Kahaner, J. Lesgourgues, J. Lesgourgues, Julien Lesgourgues, M. Abramowitz, M. Doran, M. Laine, Particle Data Group collaboration, Thomas Tram, W. Hu   +11 more
core   +1 more source

A Simpler GMRES Method for Oscillatory Integrals with Irregular Oscillations

Advances in Mathematical Physics, Volume 2015, Issue 1, 2015., 2015
A simpler GMRES method for computing oscillatory integral is presented. Theoretical analysis shows that this method is mathematically equivalent to the GMRES method proposed by Olver (2009). Moreover, the simpler GMRES does not require upper Hessenberg matrix factorization, which leads to much simpler program and requires less work.
Qinghua Wu, Meiying Xiang, Ming Mei
wiley   +1 more source

Error Bounds for the Numerical Integration of Functions with Limited Smoothness

, 2013
Recently, Trefethen (SIAM Review 50 (2008), 67--87) and Xiang and Bornemann (SIAM J. Numer. Anal. 50 (2012), 2581--2587) investigated error bounds for n-point Gauss and Clenshaw-Curtis quadrature for the Legendre weight with integrands having limited ...
Diethelm, Kai
core   +1 more source

Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants [PDF]

, 2010
We present two new adaptive quadrature routines. Both routines differ from previously published algorithms in many aspects, most significantly in how they represent the integrand, how they treat non-numerical values of the integrand, how they deal with ...
Bauer F. L., de Boor C., Henriksson S., Kahaner D. K., Ninomiya I., Pedro Gonnet, Piessens R.   +6 more
core   +1 more source

Challenges in Automatic Differentiation and Numerical Integration in Physics‐Informed Neural Networks Modelling

International Journal for Numerical Methods in Engineering, Volume 126, Issue 20, 30 October 2025.
ABSTRACT In this paper, we numerically examine the precision challenges that emerge in automatic differentiation and numerical integration in various tasks now tackled by physics‐informed neural networks (PINNs). Specifically, we illustrate how ill‐posed problems or inaccurately computed functions can cause serious precision issues in differentiation ...
Josef Daněk, Jan Pospíšil
wiley   +1 more source

On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function

Journal of Probability and Statistics, Volume 2015, Issue 1, 2015., 2015
This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval. Various combinations of downward and upward steps are handled. Numerical computation of the survival probability is done quasi‐instantaneously and with
Tristan Guillaume, Dejian Lai
wiley   +1 more source

High-accuracy numerical integration methods for fractional order derivatives and integrals computations [PDF]

, 2014
In this paper the authors present highly accurate and remarkably efficient computational methods for fractional order derivatives and integrals applying Riemann-Liouville and Caputo formulae: the Gauss-Jacobi Quadrature with adopted weight function, the ...
Brzeziński, Dariusz W., Ostalczyk, Piotr   +1 more
core   +1 more source