scholarly journals Global Extrapolation of a First Order Splitting Method

1985 ◽  
Vol 6 (3) ◽  
pp. 771-780 ◽  
Author(s):  
J. G. Verwer ◽  
H. B. de Vries
Keyword(s):  
Splitting Method ◽  
First Order ◽  
Global Extrapolation

scholarly journals A First-Order Explicit-Implicit Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 769-782
Author(s):  
Amiya K. Pani ◽  
Vidar Thomée ◽  
A. S. Vasudeva Murthy
Keyword(s):  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Second Order ◽  
Time Step ◽  
Convection Diffusion ◽  
First Order ◽  
Backward Euler ◽  
Strang Splitting ◽  
Spatially Periodic

AbstractWe analyze a second-order in space, first-order in time accurate finite difference method for a spatially periodic convection-diffusion problem. This method is a time stepping method based on the first-order Lie splitting of the spatially semidiscrete solution. In each time step, on an interval of length k, of this solution, the method uses the backward Euler method for the diffusion part, and then applies a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {\frac{k}{m}} for the convection part. With h the mesh width in space, this results in an error bound of the form {C_{0}h^{2}+C_{m}k} for appropriately smooth solutions, where {C_{m}\leq C^{\prime}+\frac{C^{\prime\prime}}{m}}. This work complements the earlier study [V. Thomée and A. S. Vasudeva Murthy, An explicit-implicit splitting method for a convection-diffusion problem, Comput. Methods Appl. Math. 19 2019, 2, 283–293] based on the second-order Strang splitting.

scholarly journals Sparse Constrained Reconstruction for Accelerating Parallel Imaging Based on Variable Splitting Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Wenlong Xu ◽  
Xiaofang Liu ◽  
Xia Li
Keyword(s):  
Magnetic Resonance ◽  
Parallel Imaging ◽  
Optimization Problems ◽  
Splitting Method ◽  
Second Order ◽  
Constrained Reconstruction ◽  
Reconstruction Process ◽  
First Order ◽  
Variable Splitting ◽  
Reconstruction Methods

Parallel imaging is a rapid magnetic resonance imaging technique. For the ill-conditioned problem, noise and aliasing artifacts are amplified during the reconstruction process and are serious especially for high accelerating imaging. In this paper, a sparse constrained reconstruction problem is proposed for parallel imaging, and an effective solution based on the variable splitting method is contrived. First-order and second-order norm optimization problems are first split, and then they are transferred to unconstrained minimization problem by the augmented Lagrangian method. At last, first-order norm and second-order norm optimization problems are alternatively resolved by different methods. With a discrepancy principle as the stopping criterion, analysis of simulated and actual parallel magnetic resonance image reconstruction is presented and discussed. Compared with the routine parallel imaging reconstruction methods, the results show that the noise and aliasing artifacts in the reconstructed image are evidently reduced at large acceleration factors.

scholarly journals Correlated Log-Normal Random Variables under a Multiscale Volatility Model

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Yong-Ki Ma
Keyword(s):  
Order Term ◽  
Operator Splitting ◽  
Splitting Method ◽  
Leading Order ◽  
First Order ◽  
Operator Splitting Method ◽  
Volatility Model ◽  
First Order Correction ◽  
Log Normal ◽  
Correction Terms

The study focuses on extending the fast mean-reversion volatility, which was developed by the author in a previous work, to the multiscale volatility model so that it can express a well-separated time scale. The leading-order term and first-order correction terms are analytically computed using the perturbation theory based on the Lie–Trotter operator splitting method. Finally, the study is concluded by deriving the numerical results that further validate the effectiveness of the model.

The Analysis of a Transmission Line Crosstalk in the Time Domain Based on First-Order Upwind

2014 ◽  
Vol 543-547 ◽  
pp. 813-816
Author(s):  
Yin Han Gao ◽  
Tian Hao Wang ◽  
Jun Dong Zhang ◽  
Kai Yu Yang ◽  
Yu Zhu
Keyword(s):  
Transmission Line ◽  
Transmission Lines ◽  
Time Domain ◽  
Splitting Method ◽  
Discontinuous Solution ◽  
Characteristic Line ◽  
First Order ◽  
The Difference ◽  
Leapfrog Scheme ◽  
The Time Domain

This article will combine the difference scheme of first-order upwind with the multi-conductor transmission lines equation to analysis the multi-conductor transmission lines crosstalk in the time domain. First-order upwind is a finite difference algorithm in the time domain; it has a first order accuracy, in the discontinuous solution there is no non-physics-oscillation, when simulate the signal. The flux splitting method which is applied to the first-order upwind solved the problem that the characteristic line direction of the wind type make plus or minus transformation along with the coefficient, make the programming simple. In this paper, simulation results of transmission line crosstalk in this algorithm will be compared with the traditional leapfrog scheme, to verify its effectiveness.

scholarly journals A Preconditioning Technique for First-Order Primal-Dual Splitting Method in Convex Optimization

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Meng Wen ◽  
Jigen Peng ◽  
Yuchao Tang ◽  
Chuanxi Zhu ◽  
Shigang Yue
Keyword(s):  
Iterative Algorithm ◽  
General Framework ◽  
Optimization Problems ◽  
Splitting Method ◽  
Iteration Process ◽  
First Order ◽  
Preconditioning Technique ◽  
Primal Dual ◽  
Preconditioned Iterative ◽  
Better Than

We introduce a preconditioning technique for the first-order primal-dual splitting method. The primal-dual splitting method offers a very general framework for solving a large class of optimization problems arising in image processing. The key idea of the preconditioning technique is that the constant iterative parameters are updated self-adaptively in the iteration process. We also give a simple and easy way to choose the diagonal preconditioners while the convergence of the iterative algorithm is maintained. The efficiency of the proposed method is demonstrated on an image denoising problem. Numerical results show that the preconditioned iterative algorithm performs better than the original one.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Stochasting modeling of planetary ring systems

1984 ◽  
Vol 75 ◽  
pp. 461-469 ◽  
Author(s):  
Robert W. Hart
Keyword(s):  
Maximum Entropy ◽  
Ring System ◽  
The Sun ◽  
Ultimate State ◽  
Interparticle Interactions ◽  
Ring Systems ◽  
First Order ◽  
Planetary Ring ◽  
Insight Into

ABSTRACTThis paper models maximum entropy configurations of idealized gravitational ring systems. Such configurations are of interest because systems generally evolve toward an ultimate state of maximum randomness. For simplicity, attention is confined to ultimate states for which interparticle interactions are no longer of first order importance. The planets, in their orbits about the sun, are one example of such a ring system. The extent to which the present approximation yields insight into ring systems such as Saturn's is explored briefly.

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