Results 191 to 200 of about 1,574 (222)
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A Hermite‐Lobatto Pseudospectral Method for Optimal Control
Asian Journal of Control, 2014AbstractA pseudospectral (PS) method based on Hermite interpolation and collocation at the Legendre‐Gauss‐Lobatto (LGL) points is presented for direct trajectory optimization and costate estimation of optimal control problems. A major characteristic of this method is that the state is approximated by the Hermite interpolation instead of the commonly ...
Liu, Yuanbo +3 more
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Pseudospectral methods for pricing options
Quantitative Finance, 2009Models with two or more risk sources have been widely applied in option pricing in order to capture volatility smiles and skews. However, the computational cost of implementing these models can be large—especially for American-style options. This paper illustrates how numerical techniques called ‘pseudospectral’ methods can be used to solve the partial
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The Bellman Pseudospectral Method
2008Based on the discoveries of a recently proposed algorithm for low-thrust trajectory optimization, we present the Bellman Pseudospectral (PS) method for a generic optimal control problem. In our original algorithm, we combined the properties of PS methods with Bellman's principle to provide an optimal solution to multi-scale and long horizon trajectory ...
Ross, I. Michael +2 more
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A generalization of the Fourier pseudospectral method
Geophysics, 2010Abstract The Fourier pseudospectral (PS) method is generalized to the case of derivatives of nonnatural order (fractional derivatives) and irrational powers of the differential operators. The generalization is straightforward because the calculation of the spatial derivatives with the fast Fourier transform is performed in the ...
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AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 2008
I. Michael Ross, Qi Gong, Pooya Sekhavat
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I. Michael Ross, Qi Gong, Pooya Sekhavat
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The rate of convergence for a pseudospectral optimal control method
2008 47th IEEE Conference on Decision and Control, 2008Over the last decade, pseudospectral (PS) methods have emerged as a popular computational solution for the problem of nonlinear constrained optimal control. They have been applied to many industrial-strength problems, notably the recent zero-propellant-maneuvering of the International Space Station performed by NASA.
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New algorithms for solving odes by pseudospectral method
Korean Journal of Computational & Applied Mathematics, 2000The paper applies results of \textit{M. T. Darvishi} and \textit{F. Ghoreishi} [ibid. 6, No. 2, 421-435 (1999; Zbl 0930.65051); Far East J. Math. Sci. (FJMS) 1, No. 2, 297-316 (1999; Zbl 0941.65014)] which compute higher derivatives for solving linear ordinary differential equations (ODEs) by using Chebyshev collocation methods with preconditioning ...
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Introduction to Spectral/Pseudospectral Methods
2015This chapter introduces the basic principles of spectral/pseudospectral methods for the solution of partial differential and/or integral equations that serve to model a large number of physical processes in chemistry and physics. The first part of the chapter defines the spectral space representation of functions and the transformation to the physical ...
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