Article
Mathematics, Applied
Ren-Jie Zhao, Tomohiro Sogabe, Tomoya Kemmochi, Shao-Liang Zhang
Summary: This article discusses the issue of selecting a suitable seed system when solving shifted linear systems and proposes a seed-switching technique to address this problem. It also introduces an improved shifted BiCGstab method and validates its effectiveness through numerical experiments.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2023)
Article
Automation & Control Systems
Soheila Ghoroghi Shafiei, Masoud Hajarian
Summary: This paper introduces the application of the Kaczmarz method in solving large-scale linear algebraic systems and Sylvester matrix equations. By deriving the matrix form and extending the algorithm, a new iterative algorithm is proposed and validated through numerical examples.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Bernhard Beckermann, Alice Cortinovis, Daniel Kressner, Marcel Schweitzer
Summary: This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) subject to low-rank modifications. The analysis shows the usefulness of the derived error bounds for guiding the choice of poles in the rational Krylov method. Additionally, a connection between low-rank updates of the matrix sign function and existing rational Krylov subspace methods is pointed out.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2021)
Article
Mathematics, Applied
Peter Chang-Yi Weng
Summary: The article discusses the solution to the large-scale nonsymmetric algebraic Riccati equation using a structure-preserving doubling algorithm. By applying the appropriate mathematical formulas and sparse plus-low-rank representations, the algorithm achieves a computational complexity of O(n) and essentially quadratic convergence.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Davide Palitta, Patrick Kuerschner
Summary: This paper introduces low-rank Krylov methods as a way to solve large-scale linear matrix equations. By improving the truncation steps, the convergence of the Krylov method is maintained, and this theoretical finding is validated through numerical experiments.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics, Applied
Daniel Kressner, Kathryn Lund, Stefano Massei, Davide Palitta
Summary: Block Krylov subspace methods are important components in modern solvers for large-scale matrix equations, and the use of restarting techniques with a compression step and dynamically adjusting basis size can effectively mitigate memory constraints in polynomial KSMs. Numerical experiments demonstrate the effectiveness of this new method compared to extended block KSMs.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
F. Bouyghf, A. Messaoudi, H. Sadok
Summary: In this paper, a comprehensive framework for studying Krylov subspace methods is presented. The mathematical properties of these methods are analyzed, their relationship with other methods is explored, and improvements are proposed. Concrete numerical examples are provided to validate the performance of the algorithms.
NUMERICAL ALGORITHMS
(2023)
Review
Thermodynamics
Tao Wei, Li-Tao Zhang
Summary: Based on the MGSSP method proposed by Huang and Huang, the authors extend and present a new NGSSP method for solving nonsymmetric saddle point problems, and analyze the convergence conditions of the corresponding matrix splitting iteration methods through theoretical analysis.
ADVANCES IN MECHANICAL ENGINEERING
(2022)
Article
Mathematics, Applied
Litao Zhang, Yifan Zhang, Xiaojing Zhang, Jianfeng Zhao
Summary: Recently, a modified shift-splitting (MSSP) preconditioner was introduced by Huang and Su [Journal of Computational and Applied Mathematics, 2017]. In this paper, an accelerated iterative method (AMSSP) is established for nonsymmetric saddle point problems based on the MSSP iteration technique. Furthermore, theoretical analysis proves the unconditional convergence of the AMSSP iteration method to the unique solution of the saddle point problems, and the spectral radius of the AMSSP iteration matrix is computed. Numerical examples demonstrate the spectrum of the new preconditioned matrix for different parameters.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2023)
Article
Mathematics, Applied
J. Alahmadi, H. Alqahtani, M. S. Pranic, L. Reichel
Summary: This paper focuses on the approximation of matrix functionals and introduces Gauss-Laurent quadrature rules for this purpose. The performance of the rules is demonstrated through computed examples.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics, Applied
T. Abe, A. T. Chronopoulos
Summary: Iterative methods, especially Krylov subspace methods (KSM), are useful for solving large and sparse linear systems problems in science and engineering modeling. Recently, nested loop KSM, such as residual cutting (RC) and generalized residual cutting (GRC), have been proposed to improve the convergence of traditional KSM. In this article, we review RC and GRC as nested loop methods for solving large and sparse linear systems problems, and demonstrate that GRC is an equivalent KSM to Orthomin with variable preconditioning. We also present a stable GRC algorithm derived using the modified Gram-Schmidt method, and show that GRC provides a general framework for constructing a class of hybrid (nested) KSM based on inner loop method selection. Numerical experiments using nonsymmetric indefinite matrices from a widely used library of sparse matrices validate the efficiency and robustness of the proposed methods.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2023)
Article
Nuclear Science & Technology
Hong-Yang Wei, Kevin Briggs, Victor Quintanilla, Yi-Tung Chen
Summary: The study developed a one-dimensional two-phase flow four-equation model to simulate the water faucet problem and evaluated the performance of different Krylov subspace methods with and without ILU preconditioner. Results showed that using ILU preconditioner improved convergence performance, with GMRES demonstrating acceptable performance without it. GMRES showed efficiency advantages with ILU preconditioner compared to other Krylov subspace methods.
NUCLEAR SCIENCE AND TECHNIQUES
(2021)
Article
Mathematics, Applied
Yuka Hashimoto, Takashi Nodera
Summary: This paper proposes a novel technique for accelerating the Krylov subspace methods for transfer operators by replacing positive definite kernels in RKHS, which is equivalent to preconditioning the transfer operator with a specific linear operator.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Takeo Hoshi, Mitsuaki Kawamura, Kazuyoshi Yoshimi, Yuichi Motoyama, Takahiro Misawa, Youhei Yamaji, Synge Todo, Naoki Kawashima, Tomohiro Sogabe
Summary: K omega is an open-source linear algebra library developed for solving a set of shifted linear equations using shifted Krylov subspace methods. It has the same operational cost as a single equation and utilizes shift invariance, demonstrating advantages in materials science applications. Benchmark calculations for excited spectra and intermediate eigenvalues show its capabilities in parallel computation for various quantum lattice models.
COMPUTER PHYSICS COMMUNICATIONS
(2021)
Article
Mathematics, Applied
Paul Escapil-Inchauspe, Carlos Jerez-Hanckes
Summary: This study extends the operator preconditioning framework to Petrov-Galerkin methods, considering parameter-dependent perturbations for both variational forms and their preconditioners. The bi-parametric abstract setting leads to robust and controlled schemes, with exhaustive convergence estimates for iterative solvers in Hilbert spaces.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Yue Qiu, Martin B. van Gijzen, Jan-Willem van Wingerden, Michel Verhaegen, Cornelis Vuik
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2018)
Article
Mathematics, Applied
Manuel Baumann, Martin B. van Gijzen
APPLIED NUMERICAL MATHEMATICS
(2019)
Article
Mathematics, Applied
R. Astudillo, J. M. de Gier, M. B. van Gijzen
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2019)
Article
Engineering, Electrical & Electronic
Aad Vijn, Eugene Lepelaars, Johan Dubbeldam, Martin van Gijzen, Arnold Heemink
IEEE TRANSACTIONS ON MAGNETICS
(2019)
Article
Engineering, Multidisciplinary
M. Pari, W. Swart, M. B. van Gijzen, M. A. N. Hendriks, J. G. Rots
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2020)
Article
Radiology, Nuclear Medicine & Medical Imaging
Emmanuel Ahishakiye, Martin Bastiaan Van Gijzen, Julius Tumwiine, Johnes Obungoloch
BMC MEDICAL IMAGING
(2020)
Article
Mathematics, Applied
Xiujie Shan, Martin B. van Gijzen
Summary: This study explores efficient implicit methods for denoising low-field MR images using a nonlinear diffusion operator as a regularizer. Different preconditioners combined with subdomain deflation are evaluated for their performance with different diffusion models. It is found that a suitable preconditioner can significantly reduce the time needed for denoising three-dimensional images, making it practical for real-world applications.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Radiology, Nuclear Medicine & Medical Imaging
David G. J. Heesterbeek, Kirsten Koolstra, Matthias J. P. van Osch, Martin B. van Gijzen, Franciscus M. Vos, Martijn A. Nagtegaal
Summary: This study proposes a method for optimizing the MR fingerprinting (MRF) sequence by taking into account both the applied undersampling pattern and a realistic reference map. By optimizing the flip angle sequence, the undersampling artifacts can be significantly reduced. Numerical simulations and in vivo measurements show that the optimized sequence exhibits better robustness against undersampling artifacts.
MAGNETIC RESONANCE IN MEDICINE
(2023)
Article
Radiology, Nuclear Medicine & Medical Imaging
Merel de Leeuw den Bouter, Martin van Gijzen, Rob Remis
Summary: This paper introduces a MRI technique based on multiplicative regularization, which effectively suppresses noise and produces accurate reconstructions.
MAGNETIC RESONANCE IMAGING
(2021)
Article
Mathematics, Applied
Yue Qiu, Martin B. van Gijzen, Jan-Willem van Wingerden, Michel Verhaegen, Cornelis Vuik
Summary: This article studies preconditioning techniques for controlling the Navier-Stokes equation with a focus on the multilevel sequentially semiseparable (MSSS) preconditioner, which demonstrates superior performance and parameter-independent convergence compared to standard block preconditioning techniques.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2021)
Proceedings Paper
Engineering, Multidisciplinary
Jan Carel Diehl, Frank van Doesum, Martien Bakker, Martin van Gijzen, Thomas O'Reilly, Ivan Muhumuza, Johnes Obungoloch, Edith Mbabazi Kabachelor
2020 IEEE GLOBAL HUMANITARIAN TECHNOLOGY CONFERENCE (GHTC)
(2020)
Proceedings Paper
Computer Science, Theory & Methods
Emmanuel Ahishakiye, Martin Bastiaan Van Gijzen, Julius Tumwiine, Johnes Obungoloch
2020 IST-AFRICA CONFERENCE (IST-AFRICA)
(2020)
Article
Multidisciplinary Sciences
Merel L. de Leeuw den Bouter, Martin B. van Gijzen, Rob F. Remis
SN APPLIED SCIENCES
(2019)
Article
Computer Science, Interdisciplinary Applications
M. Baumann, R. Astudillo, Y. Qiu, E. Y. M. Ang, M. B. van Gijzen, R. -E. Plessix
COMPUTATIONAL GEOSCIENCES
(2018)
Article
Geosciences, Multidisciplinary
Eef C. H. van Dongen, Nina Kirchner, Martin B. van Gijzen, Roderik S. W. van de Wal, Thomas Zwinger, Gong Cheng, Per Lotstedt, Lina von Sydow
GEOSCIENTIFIC MODEL DEVELOPMENT
(2018)