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Galerkin–Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds 紧黎曼流形上高斯随机场的Galerkin-Chebyshev逼近
3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-10-11 DOI: 10.1007/s10543-023-00986-8
Annika Lang, Mike Pereira
Abstract A new numerical approximation method for a class of Gaussian random fields on compact connected oriented Riemannian manifolds is introduced. This class of random fields is characterized by the Laplace–Beltrami operator on the manifold. A Galerkin approximation is combined with a polynomial approximation using Chebyshev series. This so-called Galerkin–Chebyshev approximation scheme yields efficient and generic sampling algorithms for Gaussian random fields on manifolds. Strong and weak orders of convergence for the Galerkin approximation and strong convergence orders for the Galerkin–Chebyshev approximation are shown and confirmed through numerical experiments.
摘要介绍了紧连通定向黎曼流形上一类高斯随机场的一种新的数值逼近方法。这类随机场用流形上的拉普拉斯-贝尔特拉米算子表示。伽辽金近似与切比雪夫级数的多项式近似相结合。这种所谓的Galerkin-Chebyshev近似方案为流形上的高斯随机场提供了有效和通用的采样算法。给出了Galerkin近似的强收敛阶和弱收敛阶以及Galerkin - chebyshev近似的强收敛阶,并通过数值实验加以证实。
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引用次数: 6
On the Forsythe conjecture 关于福赛斯猜想
3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-09-27 DOI: 10.1007/s10543-023-00991-x
Vance Faber, Jörg Liesen, Petr Tichý
Abstract Forsythe formulated a conjecture about the asymptotic behavior of the restarted conjugate gradient method in 1968. We translate several of his results into modern terms, and pose an analogous version of the conjecture (originally formulated only for symmetric positive definite matrices) for symmetric and nonsymmetric matrices. Our version of the conjecture uses a two-sided or cross iteration with the given matrix and its transpose, which is based on the projection process used in the Arnoldi (or for symmetric matrices the Lanczos) algorithm. We prove several new results about the limiting behavior of this iteration, but the conjecture still remains largely open. We hope that our paper motivates further research that eventually leads to a proof of the conjecture.
Forsythe(1968)提出了关于重新启动共轭梯度法渐近性的一个猜想。我们把他的一些结果翻译成现代术语,并提出了一个类似的版本的猜想(最初只表述对称正定矩阵)对称和非对称矩阵。我们的猜想版本使用给定矩阵及其转置的双边或交叉迭代,这是基于在Arnoldi(或对称矩阵Lanczos)算法中使用的投影过程。我们证明了几个关于这个迭代的极限行为的新结果,但是这个猜想在很大程度上仍然是开放的。我们希望我们的论文能激发进一步的研究,最终证明这一猜想。
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引用次数: 0
Deep neural networks on diffeomorphism groups for optimal shape reparametrization 差分同构群上最优形状再参数化的深度神经网络
3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-09-27 DOI: 10.1007/s10543-023-00989-5
Elena Celledoni, Helge Glöckner, Jørgen N. Riseth, Alexander Schmeding
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引用次数: 3
Paige’s Algorithm for solving a class of tensor least squares problem 求解一类张量最小二乘问题的Paige算法
3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-09-20 DOI: 10.1007/s10543-023-00990-y
Xue-Feng Duan, Yong-Shen Zhang, Qing-Wen Wang, Chun-Mei Li
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引用次数: 0
A stabilized finite element method on nonaffine grids for time-harmonic Maxwell’s equations 时谐麦克斯韦方程组的非仿射网格稳定有限元法
3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-09-19 DOI: 10.1007/s10543-023-00988-6
Zhijie Du, Huoyuan Duan
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引用次数: 1
Stabilized low-order mixed finite element methods for a Navier-Stokes hemivariational inequality 一类Navier-Stokes半分不等式的稳定低阶混合有限元方法
3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-09-16 DOI: 10.1007/s10543-023-00985-9
Weimin Han, Feifei Jing, Yuan Yao
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引用次数: 0
Resolving entropy growth from iterative methods 用迭代法求解熵增长
3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-09-15 DOI: 10.1007/s10543-023-00992-w
Viktor Linders, Hendrik Ranocha, Philipp Birken
Abstract We consider entropy conservative and dissipative discretizations of nonlinear conservation laws with implicit time discretizations and investigate the influence of iterative methods used to solve the arising nonlinear equations. We show that Newton’s method can turn an entropy dissipative scheme into an anti-dissipative one, even when the iteration error is smaller than the time integration error. We explore several remedies, of which the most performant is a relaxation technique, originally designed to fix entropy errors in time integration methods. Thus, relaxation works well in consort with iterative solvers, provided that the iteration errors are on the order of the time integration method. To corroborate our findings, we consider Burgers’ equation and nonlinear dispersive wave equations. We find that entropy conservation results in more accurate numerical solutions than non-conservative schemes, even when the tolerance is an order of magnitude larger.
用隐式时间离散考虑非线性守恒律的熵保守离散和耗散离散,并研究了用于求解产生的非线性方程的迭代方法的影响。我们证明了牛顿方法可以将熵耗散格式转化为反耗散格式,即使迭代误差小于时间积分误差。我们探索了几种补救措施,其中最有效的是松弛技术,最初设计用于修复时间积分方法中的熵误差。因此,只要迭代误差在时间积分法的量级上,松弛法就能很好地配合迭代求解。为了证实我们的发现,我们考虑了Burgers方程和非线性色散波动方程。我们发现,即使容差比非保守方案大一个数量级,熵守恒方案的数值解也比非保守方案精确。
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引用次数: 2
Parallel line identification for line-implicit-solvers 直线隐式求解器的平行线辨识
IF 1.5 3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-09-09 DOI: 10.1007/s10543-023-00977-9
Arne Rempke
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引用次数: 0
Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations 抛物型方程变步长时间滤波后向欧拉格式的稳定性和收敛性
IF 1.5 3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-07-03 DOI: 10.1007/s10543-023-00982-y
Hong-lin Liao, T. Tang, Tao Zhou
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引用次数: 0
Multilevel Monte Carlo using approximate distributions of the CIR process 多层蒙特卡罗使用近似分布的CIR过程
IF 1.5 3区 数学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2023-06-01 DOI: 10.1007/s10543-023-00980-0
C. Zheng
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引用次数: 0
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BIT Numerical Mathematics
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