Advances in computational mathematics Volume 51, Issue 1. A feature of this work is to exploit Jul 22, 2024 · Advances in Computational Mathematics. The main result concerns Jul 8, 2024 · In this paper, optimal estimates on the decaying rates of Jacobi expansion coefficients are obtained by fractional calculus for functions with algebraic and logarithmic singularities. Such a Advances in Computational Mathematics - Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples – in particular, the Dec 20, 2023 · In various applications, the adoption of optimal energy matching pursuit with dictionary elements is common. Volume 25 July - November 2006 Jul - Nov 2006. Volume 24 January 2006 Jan 2006. Furthermore, it is unconditionally stable in the sense that a discrete energy is dissipative when Aug 22, 2024 · This paper focuses on computing the eigenvalues of the generalized collocation matrix of the rational Said–Ball basis, also called as the quasi-rational Said–Ball–Vandermonde (q-RSBV) matrix, with high relative accuracy. Advances in Computational Mathematics. Volumes and issues. The publication process for Advances in Computational Mathematics is to publish novel innovative articles that have been extensively reviewed by competent academic peers. Compared to classical numerical methods, PINNs have several advantages, for example their ability to provide mesh-free solutions of differential equations and their ability to carry out forward and inverse modelling within the same optimisation After the success of the first Research Topic "Advances in Computational Mathematics and Statistics", we are really proud to release this second special collection dedicated to exploring this theme. A. The first algorithm is the Legendre–Gauss collocation method, which is easy to be implemented and possesses the spectral accuracy. Advances in Computational Mathematics offers a site for the dissemination of current research contributions in the rapidly growing fields of Computational Theory and Mathematics . Jun 1, 2000 · Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. This polynomial, theadjoint of the polytope, generalizes a previous two-dimensional construction described by Wachspress. Volume 48, Issue 4. This work aims to fill this gap by developing novel oracle inequalities for regularized pairwise ranking. Subject: Frames are interesting because they provide decompositions in applications where bases could be a liability. 1 day ago · Advances in Computational Mathematics publishes high quality, accessible, and original articles at the forefront of computational and applied mathematics, Scope Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. Collections listings for Advances in Computational Mathematics. We propose a statistical form of stability, defined as leave-one-out (LOO) stability. After analyzing the problem in an appropriate functional framework, we describe the method and we prove its convergence. By incorporating a pair of method parameters $$\\theta , \\eta \\in [0, 1]$$ θ , η ∈ [ 0 , 1 ] into both the drift and diffusion parts, the new schemes are indeed a kind of drift-diffusion Dec 23, 2021 · Advances in Computational Mathematics. We derive a Jul 16, 2024 · Advances in Computational Mathematics publishes high quality, accessible, and original articles at the forefront of computational and applied mathematics, Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. Dipartimento di Scienze e Innovazione Tecnologica, University of Piemonte Orientale, Viale T. The theoretical derivation indicates that the Chebyshev-Davidson method for symmetric generalized eigenvalue problems only admits local convergence; thus, in this paper, we adopt a flexible strategy to Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. This article aims to investigate a process that converts the optimal parameter selection in unbounded regions to a bounded and closed (compact) sub-domain. In this paper we derive sharp upper and lower bounds on all barycentric coordinates over convex polygons and use them to show that all such coordinates have the same continuous extension to the boundary. Aug 24, 2023 · DOI link for Advances in Computational Mathematics. Dec 7, 2022 · The efficiency of deep convolutional neural networks (DCNNs) has been demonstrated empirically in many practical applications. 50, No. Comp. Despite a wide range of applications, a rigorous theoretical demonstration still lacks to support the performance of such ranking estimators. As a demonstration, we focus on a nonlinear advection-diffusion system Nov 29, 2011 · Advances in Computational Mathematics - We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. Based on the “invariant energy quadratization” method, we propose two fully discrete time-marching Barycentric coordinates are unique for triangles, but there are many possible generalizations to convex polygons. We rely on the strong connection between wavelets and subdivision schemes to define a prediction-correction approach based on Hermite subdivision schemes that operate on manifold-valued data. We suggest to use the least solution at sparse grids with the extrema of the Dec 20, 2023 · Advances in Computational Mathematics. PREVIOUS ARTICLE. The algebraic structure of thecomplete set of regular Pythagorean-hodograph curves in ℝ3 is inherently more complicated than that of the corresponding set in ℝ2. We define a toric surface patch associated with a convex polygon, which has vertices with integer coordinates. The semigroup theory was used to demonstrate the Jun 13, 2023 · In this paper we present a construction of interpolatory Hermite multiwavelets for functions that take values in nonlinear geometries such as Riemannian manifolds or Lie groups. g. Issue 1-4 January 2006. Starting from a frame (x n) n = 1 ∞ and its arbitrary dual frame, we give sufficient conditions for constructing a dual frame of (x n) n ∈ E c so that the perfect reconstruction can be obtained from the preserved frame coefficients. Based on these criteria we will produce a series of positive definite and compactly supported radial functions, which will be very useful in applications. L. Meanwhile, a sparse fractional Fourier series for chirp $$ L Jun 4, 2022 · Advances in Computational Mathematics. Jun 23, 2023 · Advances in Computational Mathematics. Submit your manuscript. Lidia Aceto. Article MATH MathSciNet Google Scholar C. de Boor and A. Riemannian conjugate gradient method for low-rank tensor completion. Beirao da Veiga, Università di Milano-Bicocca, Italy Computational Mathematics. We invite researchers to submit original research articles, reviews, and short communications related to the above topics. Computional Mathematics Special Issue Dedicated to Charles A. Karsten Urban (Managing Editor) Ulm University, Germany Editorial Board. Ron, The least solution for the polynomial interpolation problem, Math. Search Search. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for implementation. The second algorithm is a mixture of the collocation method coupled with domain decomposition, which can be regarded as a We investigate the properties of polynomial space curvesr(t)={x(t), y(t), z(t)} whose hodographs (derivatives) satisfy the Pythagorean conditionx′2(t)+y′2(t)+z′2(t)≡σ2(t) for some real polynomial σ(t). Aug 19, 2024 · Advances in Computational Mathematics. We discuss elliptic complexes and highlight the category theoretical background and its role as a unifying language between algebraic topology, differential Oct 23, 2023 · Advances in Computational Mathematics - A fully discrete finite element method with a Gauss collocation in time is proposed for solving the nonlinear Schrödinger equation with a wave operator Advances in Computational Mathematics. The model incorporates a definition of osmosis energy that takes into account nonlocal pixel relationships using fractional derivatives and contrast change. Such a Advances in Computational Mathematics - Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples – in particular, the We provide criteria for positive definiteness of radial functions with compact support. Sep 27, 2023 · This paper studies the stochastic Allen-Cahn equation involving random diffusion coefficient field and multiplicative force noise. Finite frames avoid the subtle and omnipresent approximation problems associated with the truncation of infinite frames. Micchelli's 60th Birthday. This is inspired by the fact that integer-order derivatives fail to deal with singularity of fractional-type, while fractional calculus can. 2 Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation Oct 1, 2024 · We look at computational physics from an electrical engineering perspective and suggest that several concepts of mathematics, not so well-established in computational physics literature, present themselves as opportunities in the field. We present numerical analysis for the optimal QSC method in two space dimensions via discretizing a nonlinear time 介绍. It verifies rigorously the efficiency of DCNNs in approximating functions of many variables with some variable structures and their abilities in overcoming the curse of Jan 4, 2024 · In this paper, we study some techniques for solving numerically magnetostatic systems. Control strategies for transport networks under demand uncertainty. Covers approximation theory, numerical analysis, modelling, simulation, imaging, signal processing, and data analysis. Volume 49, Issue 4. ISSN 1019-7168; Diffusion; Title: ADVANCES IN COMPUTATIONAL MATHEMATICS related ISSN: 1572-9044 Country: Netherlands. Jul 10, 2024 · Regularized pairwise ranking with Gaussian kernels is one of the cutting-edge learning algorithms. One of the keys of randomized Kaczmarz-type Oct 15, 2021 · Advances in Computational Mathematics. Data availability and materials. It encompasses numerical modeling, the development and validation of numerical methods, and conducting numerical simulations. Normalized frames guarantee control of the frame elements. Efficient computation of the sinc matrix function for the integration of second-order differential equations. We then present a general approach for constructing such coordinates and use Advances in Computational Mathematics. The Lambert W function is defined Nov 6, 2020 · To simulate the two-phase flow of conducting fluids, we propose a coupled model of the Cahn-Hilliard equations and the inductionless and incompressible magnetohydrodynamic (MHD) equations. This As a highly interdisciplinary area, computational sciences bring together applied mathematics, statistics, computer science, mechanics etc. Special Issue Dedicated to Mariano Gasca's 60th Birthday. Sci. Volume 48, Issue 6. Volume 48, Issue 5. Both terms in the model are non-differentiable. To overcome the difficulties, we formulate the total-variation as Mar 22, 2024 · Advances in Computational Mathematics Vol. For large-scale data sets that are expensive to store and manipulate, a new variant of the discrete empirical interpolation method Dec 1, 2022 · Advances in Computational Mathematics. Ron, Computational aspects of polynomial interpolation in several variables, Math. The method is based on a Bernardi–Raugel-like Apr 7, 2022 · The edited volume includes papers in the fields of fuzzy mathematical analysis and advances in computational mathematics. For example, it plays a fundamental role in engineering, chemistry, and physics. . Solutions of learning problems by Empirical Risk Minimization (ERM) – and almost-ERM when the minimizer does not exist – need to be consistent, so that they may be predictive. 3), the author generalized the Chebyshev-Davidson method appeared in standard eigenvalue problems to symmetric generalized eigenvalue problems. Suppose that erased coefficients are indexed by a finite set E. Issue 4 November 2006; Issue 1-3 July 2006. They also need to be well-posed in the sense of being stable, so that they might be used robustly. Mar 10, 2023 · Advances in Computational Mathematics - Randomized Kaczmarz-type methods are appealing for large-scale linear systems arising from big data problems. This volume presents the refereed proceedings of the Guangzhou International Symposium on Computational Mathematics, held at the Zhongshan University, People's Republic of China. Advances in Computational Mathematics publishes high quality, accessible, and original articles at the forefront of computational and applied mathematics, Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. We use cookies to enhance your experience. Integral equation methods bring tremendous advantages for the numerical solution of a wide variety of partial differential equations in complex geometries. 1007/s10208-022-09565-9 23:3 (1043-1127) Online publication date: 14-Jun-2022 Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. A hybrid journal that publishes original articles on computational and applied mathematics, with a clear potential for impact across the sciences. Search within SPACM. S. Edited By Zhongying Chen, Yueshen Li, Charles Micchelli, Yuesheng Xu. Nearly 90 international mathematicians examine numerical optimization methods, wavelet analysis, computational approximation, numerical solutions of differential and integral equations, numerical linear algebra Jan 12, 1996 · The Lambert W(z) function is an elementar function that has been widely used in differents areas of mathematics, physics and computing science [18] [19][20][21]. Additionally, we Jul 18, 2024 · By exploiting the random sampling techniques, this paper derives an efficient randomized algorithm for computing a generalized CUR decomposition, which provides low-rank approximations of both matrices simultaneously in terms of some of their rows and columns. issn: 1019-7168 (print); 1572 Aug 9, 2024 · Let H be a separable Hilbert space and let $$\\{x_{n}\\}$$ { x n } be a sequence in H that does not contain any zero elements. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. 3 Optimally convergent mixed finite element methods for the time-dependent 2D/3D stochastic closed-loop geothermal system with multiplicative noise Aug 7, 2024 · Bibliographic content of Advances in Computational Mathematics. Home; Institute of Computational Mathematics and Scientific/Engineering Computing Category: Journal Collection Publisher: Springer Nature (Link) Description: Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. Published by Springer Nature. In this paper, we establish a theory for approximating functions from Korobov spaces by DCNNs. A peer-reviewed journal that publishes original and accessible articles on computational and applied mathematics, with a clear potential for impact across the sciences. Jun 19, 2023 · Computational mathematics is a branch of applied mathematics that focuses on solving mathematical problems using computers. Previous. Volume 50, Issue 5. We consider fairly general assumptions on the magnetic permeability tensor. Article. To achieve this, we propose explicit expressions for the minors of the q-RSBV matrix and develop a high-precision algorithm to compute these parameters. More precisely, for any given Advances in Computational Mathematics publishes high quality, accessible, and original articles at the forefront of computational and applied mathematics, Jun 8, 2010 · Advances in Computational Mathematics. It is elliptic, but can be nonhermitian. Their representations are efficient, naturally handl Jun 7, 2023 · A class of implicit Milstein type methods is introduced and analyzed in the present article for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffusion coefficients. , the perturbation terms result in the asymmetry of optimal QSC discretization. To this end, we first introduce new fractional Sobolev spaces defined Jan 25, 2024 · In this paper, we study the problem of recovering a signal from frame coefficients with erasures. Jan 29, 2018 · Many reduced-order models are neither robust with respect to parameter changes nor cost-effective enough for handling the nonlinear dependence of complex dynamical systems. Advances in Computational Mathematics - We construct a new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support. Mar 22, 2024 · Optimal quadratic spline collocation (QSC) method has been widely used in various problems due to its high-order accuracy, while the corresponding numerical analysis is rarely investigated since, e. Editors-in-Chief Alexander Barnett Flatiron Institute, New York, U. In particular, we revisit existing classical variational methods and propose new numerical methods. Comput. Manuscript Submission. Volume 50, Issue 1. (This article belongs to the Special Issue Advances in Computational and Applied Mathematics) Nov 20, 2023 · We combine the multilevel Monte Carlo (MLMC) method with a numerical scheme for the Heston model that simulates the variance process exactly or almost exactly and applies the stochastic trapezoidal rule to approximate the time-integrated variance process within the SDE of the logarithmic asset process. In Oct 27, 2022 · Advances in Computational Mathematics. A new time-stepping method based on auxiliary variable approach is proposed and analyzed. The model describes the dynamic behavior of conducting fluid under the influence of magnetic field. Published: 08 June 2010; Volume 34, pages 279–293, (2011) An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. For a particular problem, two interfaces can be used: a declarative Dec 20, 2023 · In various applications, the adoption of optimal energy matching pursuit with dictionary elements is common. Volume 48, Issue 1. Z. Our approach is based on the use of inverted finite elements and does not need any truncation. We conduct separate simulations for path-independent options and path-dependent options. 210 (1992) 347–378. We prove that for bounded loss Jul 12, 2022 · Communicated by: Paul Houston. Computational Mathematics and Statistics possess wide implications in science and engineering. The journal emphasizes three core areas: 1) approximation theory and computational geometry, 2) numerical analysis, modelling and Advances in Computational Mathematics - We study polynomial interpolation on a d-dimensional cube, where d is large. With this mostly expository work, we aim to provide a collection of the essential facts and formulae Nov 16, 2022 · Advances in Computational Mathematics - Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled C. Publishing model: Hybrid. 85 (2020), no. Volume 50, Issue 4. Stop the war! Остановите войну! solidarity - Math. With the help of these oracle inequalities, we This Special Issue will provide a platform for researchers to share their latest advances in computational mathematics and applied mathematics, as well as their applications in solving real-world problems. Its source code is mostly (85%) Python and relies on fast vectorized operations provided by the NumPy package. ADVANCES IN COMPUTATIONAL MATHEMATICS. Jan 5, 2024 · The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems, dynamic low-rank decompositions and model reduction. The method of subdivision into tensor product surfaces is Jul 31, 2023 · Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. For certain applications, further acceleration can be attained by incorporating techniques based on May 20, 2024 · The paper promotes a new sparse approximation for fractional Fourier transform, which is based on adaptive Fourier decomposition in Hardy-Hilbert space on the upper half-plane. Volume 47, Issue 5. Under this methodology, the local polynomial Fourier transform characterization of Hardy space is established, which is an analog of the Paley-Wiener theorem. ” Nowadays, with a rapid development of the computing facilities, computational statistics has been widely used for data analysis in a broad range of fields, such as actuarial science, biometrics, biomedical engineering, econometrics, environmental science, finance markets. Adaptive Fourier series—a variation of greedy algorithm. 58 (1992) 705–727. Nov 4, 2016 · The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. Volume 49, Issue 3. SlabLU: a two-level sparse direct solver for elliptic PDEs. We say that $$\\{x_{n}\\}$$ { x n } is a Bessel-normalizable or frame-normalizable sequence if the normalized sequence $${\\bigl \\{\\frac{x_n}{\\Vert x_n\\Vert }\\bigr \\}}$$ { x n ‖ x n ‖ } is a Bessel sequence or a frame for H, respectively. Home; Institute of Computational Mathematics and Scientific/Engineering Computing Feb 5, 2024 · Advances in Computational Mathematics - In this paper, we investigate a low-order robust numerical method for the linear elasticity problem. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. The proposed model was subjected to theoretical and experimental investigation. Computational science is rapidly growing, and finds important applications in a wide range of fields. We then display some computational May 8, 2024 · Advances in Computational Mathematics Vol. The numerical approximation is either based on the classical edge finite elements or on Nov 30, 2023 · Dear Colleagues, I am pleased to announce a Special Issue on “Recent Advances in Computational Statistics. NEXT ARTICLE. This rational surface patch naturally generalizes classical Bézier surfaces. Oct 21, 2011 · This paper introduces a proximity operator framework for studying the L1/TV image denoising model which minimizes the sum of a data fidelity term measured in the ℓ1-norm and the total-variation regularization term. Author contribution. Advances in Computational Mathematics - The accuracy of many schemes for interpolating scattered data with radial basis functions depends on a shape parameter c of the radial basis function. Online ISSN: 1572-9044 Oct 24, 2023 · In a recent work (J. The data and materials of the current study are available from the corresponding author upon request. The authors all contribute much effort to this work. In this paper the theory of Feb 1, 2021 · Marcati C Opschoor J Petersen P Schwab C (2022) Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities Foundations of Computational Mathematics 10. Michel, 11, 15121, Alessandria, AL, Italy Advances in Computational Mathematics. The proposed method is efficient thanks to its low computational complexity. Several features of toric patches are considered: affine invariance, convex hull property, boundary curves, implicit degree and singular points. Dedicated to Micchelli's LetPub Scientific Journal Selector (2018-2021), ADVANCES IN COMPUTATIONAL MATHEMATICS published in 1993, NETHERLANDS. This book is a comprehensive exploration of computational mathematics and its impact on enhancing the reliability and maintainability of industrial systems Advances in Computational Mathematics for Industrial System Reliability and Maintainability | SpringerLink Sep 2, 2024 · Advances in Computational Mathematics - In this paper, we show that the eigenvalues and eigenvectors of the spectral discretisation matrices resulting from the Legendre dual-Petrov-Galerkin (LDPG) Jan 17, 2024 · Advances in Computational Mathematics - The elastic transmission eigenvalue problem, arising from the inverse scattering theory, plays a critical role in the qualitative reconstruction methods for 学术期刊 Advances in Computational Mathematics，期刊 ISSN: 1019-7168, 1572-9044。ADVANCES IN COMPUTATIONAL MATHEMATICS 发表了处于计算和应用数学前沿的高质量、可访问的原创文章，具有跨科学影响的明显潜力。该杂志强调三个核心领域：近似理论和计算几何；数值分析、建模和模拟；成像、信号处理和数据分析。该 Apr 15, 2021 · Mathematics, an international, peer-reviewed Open Access journal. The journal covers approximation theory, numerical analysis, modelling, simulation, imaging, signal processing and data analysis. The fields of fuzzy mathematical analysis and advances in computational mathematics can provide valuable solutions to complex problems. May 7, 2024 · In this paper, we propose a new method for computing the stray-field and the corresponding energy for a given magnetization configuration. In this study, we put forth a robust machine learning framework for projection-based reduced-order modeling of such nonlinear and nonstationary systems. Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. This causes algorithmic difficulties for its numerical treatment. Tight frames are valuable to ensure fast convergence of such decompositions. Submission of a manuscript implies: that the work described has not been published before; that it is not under consideration for publication anywhere else; that its publication has been approved by all co-authors, if any, as well as by the responsible authorities – tacitly or explicitly – at the institute where the work has been carried out. The simplest ones arecut-off polynomials, which consist of a single polynomial piece on [0, 1] and vanish on [1, ∞). When the dictionary elements are indexed by parameters within a bounded region, exhaustion-type algorithms can be employed. In this paper Jan 8, 2024 · This paper introduces a novel model for image fusion that is based on a fractional-order osmosis approach. May 14, 2019 · SfePy (simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two, or three spatial dimensions by the finite element method. May 16, 2008 · In this paper, we propose two efficient numerical integration processes for initial value problems of ordinary differential equations. By continuing to visit this site you agree to our use of cookies. The barycentric The Advances in Computational Mathematics and Modelling (ACMM) is an interdisciplinary research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, engineering, medicine, chemistry, physics, and other areas. pcwlimh eflit tqgt pav cxoequ guej adwyq samubtt dvsd bmuv