An efficient algorithm for regularization of Laplace transform inversion in real case

Campagna, Rosanna; D’Amore, Luisa; Murli, A.

doi:10.1016/j.cam.2006.10.077

Cited by 15 publications

(5 citation statements)

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“…The chosen starting point for assimilating data is been fixed as the first of August and the first of March respectively for both subdomains. As the DA problem is an inverse ill posed problem [17,18,19], a very important topic is the choice of the regularization parameters in (5) then in (6) (see Step 6 and Step 7 of Algorithm 6). Results we carried out show as the solution of the S3DVAR software depends on these parameters in terms of both accuracy (e.g.…”

Section: The S3dvar Computational Kernelmentioning

confidence: 99%

Toward the S3DVAR data assimilation software for the Caspian Sea

Arcucci¹,

Celestino²,

Toumi³

et al. 2017

AIP Conference Proceedings

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Abstract. Data Assimilation (DA) is an uncertainty quantification technique used to incorporate observed data into a prediction model in order to improve numerical forecasted results. The forecasting model used for producing oceanographic prediction into the Caspian Sea is the Regional Ocean Modeling System (ROMS). Here we propose the computational issues we are facing in a DA software we are developing (we named S3DVAR) which implements a Scalable Three Dimensional Variational Data Assimilation model for assimilating sea surface temperature (SST) values collected into the Caspian Sea with observations provided by the Group of High resolution sea surface temperature (GHRSST). We present the algorithmic strategies we employ and the numerical issues on data collected in two of the months which present the most significant variability in water temperature: August and March.

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Section: The S3dvar Computational Kernelmentioning

confidence: 99%

Toward the S3DVAR data assimilation software for the Caspian Sea

Arcucci¹,

Celestino²,

Toumi³

et al. 2017

AIP Conference Proceedings

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“…GMRES 算法还可用于求解诸如最优控制、滤波估计、去耦、降阶等控制理论中的微分 Riccati 方程 [27] 。在大特征值问题和边值问题中会出现多元线性系统，线性控制、滤波理论、图像修复等方面包含了著名的 Lyapunov 矩阵方程、Sylvester 矩阵方程和 Stein 矩阵方程，这些方程同样是典型的多元线性系统问题，全局 GMRES 算法正好为这些问题的解决提供了一个很好的工具，不同的数值实验更显示出该方法收敛行为方面的优势 [28,29] 。 GMRES 算法还用于求解 Toeplitz 方程、Helmholtz 方程和 Navier-Stokes 方程等，预处理 GMRES 并行算法也得到了很好的应用 [30][31][32][33] 。在太阳物理的研究中，我国科学家颜毅华于 1995 年首次推导出太阳常 alpha 无力场的边界积分表示，并用边界元方法实现了数值求解 [34] ； Li 等人 2007 年对颜毅华的算法进行了改进，他们引入 GMRES 算法来解决边界元方程组；由此，对 10,000 阶以上的矩阵，用 GMRES 算法使得计算效率提高了 1000~9000 倍 [35] 。 [20] 实型 Laplace 变换的线性方程组光谱延迟修正技术 [21] 微分代数方程的初始值问题控制、光辐射和流体力学 [23][24][25][26] 近海水域控制方程、光学辐射传输方程、计算流体力学 Euler 方程控制理论 [27] 微分 Riccati 方程大型奇异值问题 [28] 广义希尔维斯特矩阵方程太阳物理研究 …”

Section: Gmres 算法的应用简况unclassified

An Overview of Recent Developments and Applications of the GMRES Method

马¹

2013

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Abstract:The generalized minimum residual method (GMRES) is widely applied in the scientific and engineering computations due to its general merit of fast convergence. This paper presents a summary introduction of the GMRES method for its historical development and practical applications, with an emphasis on its recent status. We start with a summary on the origin of the method, followed by some notable variants, together with some recent developments. Then, we introduce some recent applications of the GMRES method in various research fields, pointing out its connection to and impact on these fields. Finally, we provide an outlook on the further development and applications of the GMRES method.Keywords: GMRES; Historical Development; Practical Application

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“…D'Amore and Murli [2002] proposed an inversion algorithm based on the Fourier series expansion of the unknown function where the Fourier coefficients are approximated using a Tikhonov regularization method. Furthermore, Campagna et al [2007] highlighted that since the resulting discrete problem has a condition number that grows almost exponentially, the difficulty is the ability of extracting, only using data on the real axis, the maximum attainable accuracy on the solution.…”

Section: Introductionmentioning

confidence: 99%

Algorithm 946

D’Amore

Campagna

Mele

et al. 2014

ACM Trans. Math. Softw.

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Algorithm 662 of the ACM TOMS library is a software package, based on the Weeks method, which is used for calculating function values of the inverse Laplace transform. The software requires transform values at arbitrary points in the complex plane. We developed a software package, called ReLIADiff, which is a modification of Algorithm 662 using transform values at arbitrary points on real axis. ReLIADiff, implemented in C++, relies on TADIFF software package designed for Algorithmic Differentiation. In this article, we present ReLIADiff focusing on its design principles, performance, and use. ACM Reference Format: Luisa D'Amore, Rosanna Campagna, Valeria Mele, and Almerico Murli. 2014. Algorithm 946: ReLIADiff-A C++ software package for real Laplace transform inversion based on algorithmic differentiation. ACM Trans.

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An efficient algorithm for regularization of Laplace transform inversion in real case

Cited by 15 publications

References 5 publications

Toward the S3DVAR data assimilation software for the Caspian Sea

Toward the S3DVAR data assimilation software for the Caspian Sea

An Overview of Recent Developments and Applications of the GMRES Method

Algorithm 946

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