Article
Mathematics, Applied
Ya-Jie Liu, Xiang-Ke Chang, Yi He, Xing-Biao Hu
Summary: The first part introduces a new sequence transformation based on a special kernel and its corresponding convergence acceleration algorithm with numerical examples; the second part discusses a method to generalize the Shanks transformation via pfaffians and the corresponding recursive algorithms.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics, Applied
Xiao-Min Chen, Xiang-Ke Chang, Yi He, Xing-Biao Hu
Summary: In this paper, a generalized discrete Lotka-Volterra equation is proposed and its connections with symmetric orthogonal polynomials, Hankel determinants, and convergence acceleration algorithms are explored.
NUMERICAL ALGORITHMS
(2023)
Article
Engineering, Electrical & Electronic
L. J. Castanon, J. L. Naredo, J. R. Zuluaga, E. Banuelos-Cabral, Pablo Gomez
Summary: This paper introduces a new technique for numerical Laplace inversion which does not require truncation with a data window but instead uses Brezinski's theta algorithm to achieve consistent and high accuracy levels. Compared to the traditional technique WNLT, this new method ensures better results at lower computational costs.
ELECTRIC POWER SYSTEMS RESEARCH
(2021)
Article
Mathematics, Applied
Mengyao Gao, Xuelin Zhang, Guodong Han
Summary: The first part of this work studies the convergence rates of Kaczmarz's algorithm using abstract theorems for the convergence rate of linear operator sequences. It is proved that the algorithm converges exponentially in both default and random order, which differs from its slow behavior in practice. The second part proposes a new scheme with reordered rays in image reconstruction, and numerical experiments show that it outperforms previous schemes in the literature.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
C. Brezinski, M. Redivo-Zaglia
Summary: Sequence transformation can accelerate the convergence of slow-converging scalar sequences and even be applied to diverging sequences for analytic continuation. Shanks' transformation is a well-known method for accelerating convergence, with various extensions and implementations demonstrating its effectiveness in applications.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
Hai-qiong Zhao, Tong Zhou
Summary: This letter presents a four-component Volterra lattice (FCVL) hierarchy and its first flow, i.e., FCVL system, using the discrete zero curvature representation and a 4x4 matrix spectral problem with four potential functions. Additionally, a Darboux transformation for the FCVL system is established through the gauge transformation between the corresponding 4x4 matrix spectral problems, leading to the derivation of exact solutions in various cases.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Computer Science, Software Engineering
Sabyasachi Mukherjee, Sayan Mukherjee, Binh-Son Hua, Nobuyuki Umetani, Daniel Meister
Summary: Monte Carlo integration is a technique for numerically estimating definite integrals by randomly sampling the integrand, but the convergence rate of its estimates slows down as more samples are drawn. To accelerate the convergence rate, sequence transformations can be applied, but analytically finding such transformations can be challenging due to the stochastic nature and complexity of the integrand.
COMPUTER GRAPHICS FORUM
(2021)
Article
Operations Research & Management Science
Radu Ioan Bot, Erno Robert Csetnek, Michael Sedlmayer
Summary: In this paper, a novel algorithm named OGAProx is proposed to solve the convex-concave saddle point problem, and its convergence and convergence rate are verified under different situations. The algorithm combines optimistic gradient ascent step and proximal step, and is validated in practical problems.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Article
Automation & Control Systems
Xin He, Rong Hu, Ya-Ping Fang
Summary: In this paper, a fast primal-dual algorithm is proposed for convex optimization problems with linear equality constraints. The algorithm demonstrates fast convergence rates for the objective residual and the feasibility violation, and numerical experiments confirm its effectiveness.
Article
Mathematics, Applied
Claude Brezinski, Stefano Cipolla, Michela Redivo-Zaglia, Yousef Saad
Summary: This paper investigates extrapolation and acceleration methods and introduces modified Shanks transformation for handling general sequences. The goal of the paper is to establish a general framework that encompasses most known acceleration strategies. The paper also explores Anderson Acceleration method in connection with quasi-Newton methods to establish local linear convergence results of its stabilized version. The methods are tested on various problems, including those arising from nonlinear partial differential equations.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Xiaohua Ma, Chengming Huang
Summary: This paper rigorously analyzes the exponential convergence of the Chebyshev collocation method for third kind linear Volterra integral equations, utilizing a smoothing transformation to overcome singularity issues at the beginning of time. The numerical method achieves spectral accuracy and is demonstrated to be applicable and efficient through examples with non-smooth solutions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Suzan Cival Buranay
Summary: This research focuses on a class of two-dimensional fractional Volterra integral equations (2D-FVIEs) of the second kind. Smoothing transformations are used to improve the regularity of the original 2D-FVIEs, as the solution may have unbounded derivatives near the integral domain boundary. The novelty lies in the theoretical investigation and numerical application of the bivariate modified Bernstein-Kantorovich (B-MBK) operators for approximating the unknown solution of 2D-FVIEs. An algorithm utilizing the B-MBK operators and discretization is provided to approximate the solution of the transformed discretized equation, followed by an inverse transformation to obtain the solution of the original equation. The applicability of the proposed method is demonstrated through examples from literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Shuai Wang, Bingdong Li, Aimin Zhou
Summary: This paper proposes an efficient regularity augmented evolutionary algorithm (RAEA) for multiobjective optimization, which extracts latent spaces using singular value decomposition and enhances convergence acceleration and dual-space search strategy.
SWARM AND EVOLUTIONARY COMPUTATION
(2023)
Article
Computer Science, Artificial Intelligence
Tao Sun, Dongsheng Li
Summary: This paper considers a class of nonconvex regularized optimization problems and proposes an accelerated algorithm. The algorithm inherits the advantages of decentralized algorithms and is proven to converge.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
(2022)
Article
Mathematics, Applied
R. Katani, S. McKee
Summary: Various numerical methods have been proposed for solving weakly singular Volterra integral equations, but this paper focuses on a method for solving two-dimensional nonlinear weakly singular Volterra integral equations of the second kind. By applying a simple smoothing change of variables and employing Navot's quadrature rule, the transformed integral equation is solved with smooth solutions. Theoretical results are verified through numerical examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Claude Brezinski, Kathy A. Driver, Michela Rediyo-Zaglia
APPLIED NUMERICAL MATHEMATICS
(2019)
Article
Mathematics, Applied
Claude Brezinski, Michela Redivo-Zaglia
NUMERICAL ALGORITHMS
(2019)
Article
Mathematics
Claude Brezinski, Michela Redivo-Zaglia
ELECTRONIC JOURNAL OF LINEAR ALGEBRA
(2019)
Article
Mathematics, Applied
Claude Brezinski, Michela Redivo-Zaglia
NUMERICAL ALGORITHMS
(2020)
Article
Mathematics, Applied
Stefano Cipolla, Michela Redivo-Zaglia, Francesco Tudisco
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2020)
Article
Mathematics
Claude Brezinski, F. Alexander Norman, Michela Redivo-Zaglia
Summary: After the death of Peter Wynn in December 2017, manuscript documents he left were found, covering topics such as continued fractions, rational approximation, interpolation, orthogonal polynomials, moment problems, series, and abstract algebra. Some of the documents are nearly complete and ready for publication, while others require further work. These works are seen as valuable additions to the existing literature on these topics and may lead to new research and results. Two previously unpublished papers are also mentioned for the first time in this paper.
Article
Mathematics, Applied
Claude Brezinski, Michela Redivo-Zaglia
Summary: The aim of this paper is to propose a general theoretical framework for extrapolation and prediction of sequences in a vector space. Specific cases are studied and recursive algorithms for implementing some of the procedures are discussed. Possible extensions of this work are also mentioned.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Claude Brezinski, Michela Redivo-Zaglia, Ahmed Salam
Summary: This paper proves that the sufficient condition characterizing the vector epsilon-algorithm's kernel sequence is not necessary, and presents the formula for the vector epsilon(2)-transformation and its kernel sequence's expressions.
NUMERICAL ALGORITHMS
(2023)
Editorial Material
Mathematics, Applied
Michela Redivo-Zaglia
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Stefano Cipolla, Stefano Pozza, Michela Redivo-Zaglia, Niel Van Buggenhout
Summary: This paper presents a new framework for the computation of bilinear forms involving the time-ordered exponential and studies its theoretical properties. The effectiveness of the approach is confirmed through computational results on real-world problems.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Claude Brezinski, Stefano Cipolla, Michela Redivo-Zaglia, Yousef Saad
Summary: This paper investigates extrapolation and acceleration methods and introduces modified Shanks transformation for handling general sequences. The goal of the paper is to establish a general framework that encompasses most known acceleration strategies. The paper also explores Anderson Acceleration method in connection with quasi-Newton methods to establish local linear convergence results of its stabilized version. The methods are tested on various problems, including those arising from nonlinear partial differential equations.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2022)
Article
Mathematics, Applied
C. Brezinski, M. Redivo-Zaglia
Summary: Sequence transformation can accelerate the convergence of slow-converging scalar sequences and even be applied to diverging sequences for analytic continuation. Shanks' transformation is a well-known method for accelerating convergence, with various extensions and implementations demonstrating its effectiveness in applications.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
(2021)
Article
Mathematics, Applied
Stefano Cipolla, Michela Redivo-Zaglia, Francesco Tudisco
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
(2020)
Article
Mathematics, Applied
Claude Brezinski, Michela Redivo-Zaglia
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS
(2019)
Article
Mathematics
C. Brezinski, M. Redivo-Zaglia
REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES
(2018)
