The Experts below are selected from a list of 17379 Experts worldwide ranked by ideXlab platform
Rados Radoicic - One of the best experts on this subject based on the ideXlab platform.
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Rational Approximation of the rough heston solution
International Journal of Theoretical and Applied Finance, 2019Co-Authors: Jim Gatheral, Rados RadoicicAbstract:Pricing in the rough Heston model of Jaisson & M. Rosenbaum [(2016) Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes, The Annals of Applied Probability...
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Rational Approximation of the rough heston solution
Social Science Research Network, 2019Co-Authors: Jim Gatheral, Rados RadoicicAbstract:We present a simple Rational Approximation to the solution of the rough Heston Riccati equation valid in a region of its domain relevant to option valuation. Pricing under rough Heston using this Approximation is both fast and very accurate.
Jim Gatheral - One of the best experts on this subject based on the ideXlab platform.
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Rational Approximation of the rough heston solution
International Journal of Theoretical and Applied Finance, 2019Co-Authors: Jim Gatheral, Rados RadoicicAbstract:Pricing in the rough Heston model of Jaisson & M. Rosenbaum [(2016) Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes, The Annals of Applied Probability...
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Rational Approximation of the rough heston solution
Social Science Research Network, 2019Co-Authors: Jim Gatheral, Rados RadoicicAbstract:We present a simple Rational Approximation to the solution of the rough Heston Riccati equation valid in a region of its domain relevant to option valuation. Pricing under rough Heston using this Approximation is both fast and very accurate.
Tom Dhaene - One of the best experts on this subject based on the ideXlab platform.
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Advancements in Iterative Methods for Rational Approximation in the Frequency Domain
IEEE Transactions on Power Delivery, 2007Co-Authors: Dirk Deschrijver, B. Gustavsen, Tom DhaeneAbstract:Rational Approximation of frequency-domain responses is commonly used in electromagnetic transients programs for frequency-dependent modeling of transmission lines and to some extent, network equivalents (FDNEs) and transformers. This paper analyses one of the techniques [vector fitting (VF)] within a general iterative least-squares scheme that also explains the relation with the polynomial-based Sanathanan-Koerner iteration. Two recent enhancements of the original VF formulation are described: orthonormal vector fitting (OVF) which uses orthonormal functions as basis functions instead of partial fractions, and relaxed vector fitting (RVF), which uses a relaxed least-squares normalization for the pole identification step. These approaches have been combined into a single approach: relaxed orthonormal vector fitting (ROVF). The application to FDNE identification shows that ROVF offers more robustness and better convergence than the original VF formulation. Alternative formulations using explicit weighting and total least squares are also explored.
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a discussion of Rational Approximation of frequency domain responses by vector fitting
IEEE Transactions on Power Systems, 2006Co-Authors: W Hendrickx, Tom DhaeneAbstract:Vector fitting (VF) is a popular iterative Rational Approximation technique for sampled data in the frequency domain. VF is nowadays widely investigated and used in the Power Systems and Microwave Engineering communities. The VF methodology is recognized as an elegant version of the Sanathanan-Koerner iteration with a well-chosen basis.
Joseph E Pasciak - One of the best experts on this subject based on the ideXlab platform.
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analysis of numerical methods for spectral fractional elliptic equations based on the best uniform Rational Approximation
Journal of Computational Physics, 2020Co-Authors: Stanislav Harizanov, Raytcho Lazarov, Svetozar Margenov, Pencho Marinov, Joseph E PasciakAbstract:Abstract Here we study theoretically and compare experimentally with the methods developed in [1] , [2] an efficient method for solving systems of algebraic equations A ˜ α u ˜ h = f ˜ h , 0 α 1 , where A ˜ is an N × N matrix coming from the discretization of a fractional diffusion operator. More specifically, we focus on matrices obtained from finite difference or finite element Approximation of second order elliptic problems in R d , d = 1 , 2 , 3 . The proposed methods are based on the best uniform Rational Approximation (BURA) r α , k ( t ) of t α on [ 0 , 1 ] . Here r α , k is a Rational function of t involving numerator and denominator polynomials of degree at most k. The Approximation of u ˜ h = A ˜ − α f ˜ h is then w ˜ h = λ 1 − α r α , k ( λ 1 A ˜ − 1 ) f ˜ h , where λ 1 is the smallest eigenvalue of A ˜ . We show that the proposed method is exponentially convergent with respect to k and has some attractive properties. First, it reduces the solution of the nonlocal system to solution of k systems with matrix ( A ˜ + c j I ˜ ) and c j > 0 , j = 1 , 2 , … , k . Thus, good computational complexity can be achieved if fast solvers are available for such systems. Second, the original problem and its Rational Approximation in the finite difference case are positivity preserving. In the finite element case, this valid for schemes obtained by mass lumping under certain mild conditions on the mesh. Further, we prove that the lumped mass schemes still have the expected rate of convergence, at times assuming additional regularity on the right hand side. Finally, we present comprehensive numerical experiments on a number of model problems for various α in one and two spatial dimensions. These illustrate the computational behavior of the proposed method and compare its accuracy and efficiency with that of other methods developed by Harizanov et al. [1] and Bonito and Pasciak [2] .
Maria Pusa - One of the best experts on this subject based on the ideXlab platform.
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improving the accuracy of the chebyshev Rational Approximation method using substeps
Nuclear Science and Engineering, 2016Co-Authors: Aarno Isotalo, Maria PusaAbstract:The Chebyshev Rational Approximation method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step ...
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solving linear systems with sparse gaussian elimination in the chebyshev Rational Approximation method
Nuclear Science and Engineering, 2013Co-Authors: Maria Pusa, Jaakko LeppanenAbstract:AbstractThe Chebyshev Rational Approximation Method (CRAM) has recently been introduced by the authors to solve burnup equations, and the results have been excellent. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices, and it can be characterized as the best Rational Approximation on the negative real axis. The coefficients of the Rational Approximation are fixed and have been reported for various Approximation orders. In addition to these coefficients, implementing the method requires only a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM Approximation. The introduced direct method is based on sparse Gaussian elimination, where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of t...
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correction to partial fraction decomposition coefficients for chebyshev Rational Approximation on the negative real axis
arXiv: Numerical Analysis, 2012Co-Authors: Maria PusaAbstract:Chebyshev Rational Approximation can be a viable method to compute the exponential of matrices with eigenvalues in the vicinity of the negative real axis, and it was recently applied successfully to solving nuclear fuel burnup equations. Determining the partial fraction decomposition (PFD) coefficients of this Approximation can be difficult and they have been provided (for Approximation orders 10 and 14) by Gallopoulos and Saad in "Efficient solution of parabolic equations by Krylov Approximation methods", SIAM J. Sci. Stat. Comput., 13(1992). It was recently discovered that the order 14 coefficients contain errors and result in 100 times poorer accuracy than expected by theory. The purpose of this note is to provide the correct PFD coefficients for Approximation orders 14 and 16 and to briefly discuss the Approximation accuracy resulting from the erroneous coefficients.
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Rational Approximations to the matrix exponential in burnup calculations
Nuclear Science and Engineering, 2011Co-Authors: Maria PusaAbstract:AbstractThe topic of this paper is solving the burnup equations using dedicated matrix exponential methods that are based on two different types of Rational Approximation near the negative real axis. The previously introduced Chebyshev Rational Approximation Method (CRAM) is now analyzed in detail for its accuracy and convergence, and correct partial fraction coefficients for Approximation orders 14 and 16 are given to facilitate its implementation and improve the accuracy. As a new approach, Rational Approximation based on quadrature formulas derived from complex contour integrals is proposed, which forms an attractive alternative to CRAM, as its coefficients are easy to compute for any order of Approximation. This gives the user the option to routinely choose between computational efficiency and accuracy all the way up to the level permitted by the available arithmetic precision. The presented results for two test cases are validated against reference solutions computed using high-precision arithmetics....
