SIAM Journal on Numerical Analysis最新文献_第3页

From Characteristic Functions to Multivariate Distribution Functions and European Option Prices by the (Damped) COS Method 从特征函数到多元分布函数与欧式期权价格的（阻尼）COS方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-12-17 DOI: 10.1137/24m1666240

Gero Junike, Hauke Stier

{"title":"From Characteristic Functions to Multivariate Distribution Functions and European Option Prices by the (Damped) COS Method","authors":"Gero Junike, Hauke Stier","doi":"10.1137/24m1666240","DOIUrl":"https://doi.org/10.1137/24m1666240","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 6, Page 2421-2453, December 2025. Abstract. We provide a unified framework to obtain numerically certain quantities, such as the distribution function, absolute moments, and prices of financial options, from the characteristic function of some (unknown) probability density function using the Fourier-cosine series (COS) method. The classical COS method is numerically very efficient in one dimension, but it cannot deal very well with certain integrands in general dimensions. Therefore, we introduce the damped COS method, which can handle a large class of integrands very efficiently. We prove the convergence of the (damped) COS method and study its order of convergence. The method converges exponentially if the characteristic function decays exponentially. To apply the (damped) COS method, one has to specify two parameters: a truncation range for the multivariate density and the number of terms to approximate the truncated density by a COS. We provide an explicit formula for the truncation range and an implicit formula for the number of terms. Numerical experiments up to five dimensions confirm the theoretical results.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"157 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145771639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fast Supremizer Method on Penalty-Based Reduced-Order Modeling for Incompressible Flows 基于惩罚的不可压缩流降阶建模的快速优化方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-12-17 DOI: 10.1137/25m1746112

Hui Yao, Mejdi Azaiez

{"title":"Fast Supremizer Method on Penalty-Based Reduced-Order Modeling for Incompressible Flows","authors":"Hui Yao, Mejdi Azaiez","doi":"10.1137/25m1746112","DOIUrl":"https://doi.org/10.1137/25m1746112","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 6, Page 2483-2511, December 2025. Abstract. The supremizer method enriches the reduced velocity basis for pressure recovery in incompressible flows, ensuring the inf-sup condition in the reduced space. In the full-order model, a small penalty term is often introduced to prevent spurious modes [Y. He, Math. Comp., 74 (2005), pp. 1201–1216] and is also essential for accuracy in the proper orthogonal decomposition–based reduced-order model [A.-L. Gerner and K. Veroy, Math. Models Methods Appl. Sci., 21 (2011), pp. 2103–2134]. However, coupling pressure and velocity, along with the supremizer basis, significantly increases the computational costs in both offline and online phases. We find that the primary role of supremizers is to improve stability, rather than velocity accuracy. We propose a novel method using several supremizers for the velocity basis, decoupling the penalized system to solve for velocity. The full set of supremizers is then used to recover pressure. This strategy reduces the computational cost while maintaining stability and accuracy. We derive error estimates using a supremizer-augmented projection operator, which depend on the inf-sup constant rather than on the inverse of the penalty coefficient. We also develop two new supremizer construction options satisfying the inf-sup condition, one of which avoids solving the full-order equations for obtaining supremizer basis, further reducing offline costs. Numerical experiments demonstrate the effectiveness of the proposed method. For comparable accuracy, CPU time tests show that the online computational cost is reduced by about [math], and the offline assembly cost by [math], compared to [Y. He, Math. Comp., 74 (2005), pp. 1201–1216].","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"82 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145771690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

High-Order Integration on Regular Triangulated Manifolds Reaches Superalgebraic Approximation Rates Through Cubical Reparametrizations 正则三角化流形上的高阶积分通过三次再参数化达到超代数逼近率

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-12-17 DOI: 10.1137/24m1707274

Gentian Zavalani, Oliver Sander, Michael Hecht

{"title":"High-Order Integration on Regular Triangulated Manifolds Reaches Superalgebraic Approximation Rates Through Cubical Reparametrizations","authors":"Gentian Zavalani, Oliver Sander, Michael Hecht","doi":"10.1137/24m1707274","DOIUrl":"https://doi.org/10.1137/24m1707274","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 6, Page 2454-2482, December 2025. Abstract. We present a novel methodology for deriving high-order volume elements (HOVE) designed for the integration of scalar functions over regular embedded manifolds. For constructing HOVE, we introduce square-squeezing—a homeomorphic multilinear hypercube-simplex transformation—reparametrizing an initial flat triangulation of the manifold to a cubical mesh. By employing square-squeezing, we approximate the integrand and the volume element for each hypercube domain of the reparametrized mesh through interpolation in Chebyshev–Lobatto grids. This strategy circumvents the Runge phenomenon, replacing the initial integral with a closed-form expression that can be precisely computed by high-order quadratures. We prove novel bounds of the integration error in terms of the [math]-order total variation of the integrand and the surface parametrization, predicting high algebraic approximation rates that scale solely with the interpolation degree and not, as is common, with the average simplex size. For smooth integrals whose total variation is constantly bounded with increasing [math], the estimates prove the integration error to decrease even exponentially, while mesh refinements are limited to achieve algebraic rates. The resulting approximation power is demonstrated in several numerical experiments, particularly showcasing [math]-refinements to overcome the limitations of [math]-refinements for highly varying smooth integrals.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"111 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145771636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Posteriori Error Estimates for Schrödinger Operators Discretized with Linear Combinations of Atomic Orbitals 原子轨道线性组合离散Schrödinger算子的后验误差估计

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-12-16 DOI: 10.1137/24m1700697

Mi-Song Dupuy, Geneviève Dusson, Ioanna-Maria Lygatsika

引用次数: 0

Numerical Schemes for Signature Kernels 签名核的数值格式

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-12-11 DOI: 10.1137/25m1740681

Thomas Cass, Francesco Piatti, Jeffrey Pei

{"title":"Numerical Schemes for Signature Kernels","authors":"Thomas Cass, Francesco Piatti, Jeffrey Pei","doi":"10.1137/25m1740681","DOIUrl":"https://doi.org/10.1137/25m1740681","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 6, Page 2371-2394, December 2025. Abstract. Signature kernels have become a powerful tool in kernel methods for sequential data. In “The Signature Kernel is the solution of a Goursat PDE” [], the authors introduced a kernel trick showing that, for continuously differentiable paths, the signature kernel satisfies a hyperbolic PDE of Goursat type in two independent time variables. While finite difference methods have been explored for this PDE, they suffer from accuracy and stability issues when handling highly oscillatory inputs. In this work, we propose two advanced numerical schemes that approximate the solution using polynomial representations of boundary conditions and employing either approximation or interpolation techniques. We prove the convergence of the polynomial approximation scheme and demonstrate experimentally that both methods achieve several orders of magnitude improvement in mean absolute percentage error (MAPE) over finite difference schemes without increasing computational complexity. These algorithms are implemented in a publicly available Python library: https://github.com/FrancescoPiatti/polysigkernel.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"15 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145718456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized Gentlest Ascent Dynamics Methods for High-Index Saddle Points 高指数鞍点的广义最平缓上升动力学方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-11-19 DOI: 10.1137/24m1710905

Moody T. Chu, Matthew M. Lin

{"title":"Generalized Gentlest Ascent Dynamics Methods for High-Index Saddle Points","authors":"Moody T. Chu, Matthew M. Lin","doi":"10.1137/24m1710905","DOIUrl":"https://doi.org/10.1137/24m1710905","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 6, Page 2343-2370, December 2025. Abstract. A geometric perspective on the gentlest ascent dynamics is presented, revealing that the dynamics is utilizing the Householder reflector—constructed via the continuous power method—to adapt the negative gradient and identify index-1 saddle points. While the adaptation appears intuitive, it is governed by a precise criterion. Building on this geometric insight, three generalized dynamical systems are introduced for locating high-index saddle points, each centered on estimating directions for constructing generalized reflectors. The first approach employs the Oja flow to evolve eigenspaces, encompassing the continuous power method as a special case. The second approach formulates a matrix Riccati differential equation for the projector operator on the Grassmann manifold, which is shown to be equivalent to a double bracket flow with inherent sorting properties. The third approach is a hybrid method based on conventional subspace iteration, incorporating [math] factorization for normalization. The equilibrium points of all three systems are classified, and convergence analyses are provided. These dynamical systems are readily solvable by using high-precision numerical ODE integrators. Numerical experiments confirm the theoretical results.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"40 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145559903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Reynolds-Semirobust Method with Hybrid Velocity and Pressure for the Unsteady Incompressible Navier–Stokes Equations 非定常不可压缩Navier-Stokes方程的速度和压力混合reynolds -半鲁棒方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-11-17 DOI: 10.1137/25m1736104

L. Beirão da Veiga, D. A. Di Pietro, J. Droniou, K. B. Haile, T. J. Radley

引用次数: 0

Boundary-Value Problems of Functional Differential Equations with State-Dependent Delays 状态相关时滞泛函微分方程的边值问题

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-11-11 DOI: 10.1137/24m1711182

Alessia Andò, Jan Sieber

引用次数: 0

An Efficient Finite Element Method for the Quad-Curl Problem 求解四旋度问题的一种有效有限元方法

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-11-07 DOI: 10.1137/24m166022x

Jingzhi Li, Shipeng Mao, Chao Wang, Zhimin Zhang

{"title":"An Efficient Finite Element Method for the Quad-Curl Problem","authors":"Jingzhi Li, Shipeng Mao, Chao Wang, Zhimin Zhang","doi":"10.1137/24m166022x","DOIUrl":"https://doi.org/10.1137/24m166022x","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 6, Page 2272-2295, December 2025. Abstract. The quad-curl problem is a critical issue in magnetohydrodynamics and inverse electromagnetic scattering theory. It has traditionally been addressed by most existing numerical schemes through the formation of saddle-point systems, thereby introducing substantial challenges for both theoretical analysis and practical numerical implementations. This study introduces a novel regularization-based approach that diverges from these conventional methods, specifically designed to avoid the saddle-point issue. The challenge of addressing the divergence-free constraint in finite element methods is tackled in a unique way. Moreover, it ensures a consistent well-posedness, leading to a symmetric, positive-definite system in finite element discretization, which simplifies the implementation process. The regularized problem is addressed using the conforming finite element method, employing [math]-conforming element, and the discontinuous Galerkin method, utilizing Nédélec’s element, both of which achieve quasi-optimal error bounds in relevant norms. The efficiency of our proposed methods is further demonstrated through a series of numerical experiments in both two and three dimensions.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"114 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145462322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Convergence Analysis Of Lawson’s Iteration For Computing Polynomial And Rational Minimax Approximations 计算多项式和有理极大极小逼近的Lawson迭代收敛性分析

IF 2.9 2区数学

SIAM Journal on Numerical Analysis Pub Date : 2025-11-07 DOI: 10.1137/24m1708814

Lei-Hong Zhang, Shanheng Han

{"title":"A Convergence Analysis Of Lawson’s Iteration For Computing Polynomial And Rational Minimax Approximations","authors":"Lei-Hong Zhang, Shanheng Han","doi":"10.1137/24m1708814","DOIUrl":"https://doi.org/10.1137/24m1708814","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 6, Page 2249-2271, December 2025. Abstract. Lawson’s iteration is a classical and effective method for solving the linear (polynomial) minimax approximation problem in the complex plane. Extension of Lawson’s iteration for the rational minimax approximation problem with both computationally high efficiency and theoretical guarantee is challenging. The recent work [L.-H. Zhang et al., Math. Comp., 94 (2025), pp. 2457–2494] reveals that Lawson’s iteration can be viewed as a method for solving the dual problem of the original rational minimax approximation problem, and the work proposes a new type of Lawson’s iteration, namely, d-Lawson, which reduces to the classical Lawson’s iteration for the linear minimax approximation problem. For the rational case, such a dual problem is guaranteed to obtain the original minimax solution under Ruttan’s sufficient condition, and, numerically, d-Lawson was observed to converge monotonically with respect to the dual objective function. In this paper, we present a theoretical convergence analysis of d-Lawson for both the linear and rational minimax approximation problems. In particular, we show that (i) for the linear minimax approximation problem, [math] is a near-optimal Lawson exponent in Lawson’s iteration; and (ii) for the rational minimax approximation problem, under certain conditions, d-Lawson converges monotonically with respect to the dual objective function for any sufficiently small [math], and the limiting approximant satisfies the complementary slackness condition which states that any node associated with positive weight is either an interpolation point or has a constant error.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"10 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145455188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0