scholarly journals A Simpler GMRES Method for Oscillatory Integrals with Irregular Oscillations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Qinghua Wu ◽  
Meiying Xiang
Keyword(s):  
Theoretical Analysis ◽  
Matrix Factorization ◽  
Numerical Experiments ◽  
Oscillatory Integral ◽  
Oscillatory Integrals ◽  
New Method ◽  
Gmres Method ◽  
Hessenberg Matrix

A simpler GMRES method for computing oscillatory integral is presented. Theoretical analysis shows that this method is mathematically equivalent to the GMRES method proposed by Olver (2009). Moreover, the simpler GMRES does not require upper Hessenberg matrix factorization, which leads to much simpler program and requires less work. Numerical experiments are conducted to illustrate the performance of the new method and show that in some cases the simpler GMRES method could achieve higher accuracy than GMRES.

scholarly journals ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150193 ◽  
Author(s):  
Ingrid Daubechies ◽  
Yi (Grace) Wang ◽  
Hau-tieng Wu
Keyword(s):  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Time Dependent ◽  
New Method ◽  
Time Varying ◽  
Frequency Content ◽  
Time Frequency ◽  
Instantaneous Frequencies

A new method is proposed to determine the time–frequency content of time-dependent signals consisting of multiple oscillatory components, with time-varying amplitudes and instantaneous frequencies. Numerical experiments as well as a theoretical analysis are presented to assess its effectiveness.

scholarly journals On preconditioned normal and skew-Hermitian splitting iteration method for continuous Sylvester equations AX + XB = C*

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2207-2217
Author(s):  
Xue-Qing Liang ◽  
Xiang Wang ◽  
Xiao-Bin Tang ◽  
Xiao-Yong Xiao
Keyword(s):  
Exact Solution ◽  
Theoretical Analysis ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Convergence Property ◽  
Positive Definite ◽  
New Method ◽  
Splitting Iteration Method

In this paper, we present a preconditioned normal and skew-Hermitian splitting (PNSS) iteration method for continuous Sylvester equations AX + XB = C with positive definite/semi-definite matrices. Theoretical analysis shows that the PNSS methods will converge unconditionally to the exact solution of the continuous Sylvester equations. An inexact variant of the PNSS iteration method(IPNSS) and the analysis of its convergence property in detail have been established. Numerical experiments further show that this new method is more efficient and robust than the existing ones.

SINS Installation Error Calibration Based on Multi-Position Combinations

2011 ◽  
Vol 383-390 ◽  
pp. 4213-4220
Author(s):  
Zhen Huan Wang ◽  
Xi Jun Chen ◽  
Qing Shuang Zeng
Keyword(s):  
Theoretical Analysis ◽  
Least Squares ◽  
Rotation Rate ◽  
Scale Factor ◽  
New Method ◽  
Earth’S Rotation ◽  
Earth's Rotation ◽  
Error Calibration ◽  
Sine And Cosine Functions ◽  
Cosine Functions

A new method is proposed to calibrate the installation errors of SINS. According to the method, the installation errors of the gyro and accelerometer can be calibrated simultaneously, which not depend on latitude, gravity, scale factor and earth's rotation rate. By the multi-position combinations, the installation errors of the gyro and accelerometer are modulated into the sine and cosine functions, which can be identified respectively based on the least squares. In order to verify the correctness of the theoretical analysis, the SINS is experimented by a three-axis turntable, and the installation errors of the gyro and accelerometer are identified respectively according to the proposed method. After the compensation of the installation error, the accuracy of the SINS is improved significantly.

scholarly journals Multivalued Discrete Tomography Using Dynamical System That Describes Competition

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Takeshi Kojima ◽  
Tetsushi Ueta ◽  
Tetsuya Yoshinaga
Keyword(s):  
Dynamical System ◽  
Theoretical Analysis ◽  
Continuous Time ◽  
Numerical Experiments ◽  
Nonlinear Dynamical System ◽  
Reconstructed Image ◽  
Optimization Approach ◽  
Discrete Tomography ◽  
Nonlinear Dynamical ◽  
Time Optimization

Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown.

scholarly journals Performance Analysis of Maximum Likelihood Estimation for Transmit Power Based on Signal Strength Model

2018 ◽  
Vol 7 (3) ◽  
pp. 38 ◽  
Author(s):  
Xiao-Li Hu ◽  
Pin-Han Ho ◽  
Limei Peng
Keyword(s):  
Maximum Likelihood ◽  
Performance Analysis ◽  
Theoretical Analysis ◽  
Numerical Experiments ◽  
Likelihood Estimation ◽  
Signal Strength ◽  
Strength Model ◽  
Transmit Power ◽  
Ml Estimation ◽  
Theoretical Performance

We study theoretical performance of Maximum Likelihood (ML) estimation for transmit power of a primary node in a wireless network with cooperative receiver nodes. The condition that the consistence of an ML estimation via cooperative sensing can be guaranteed is firstly defined. Theoretical analysis is conducted on the feasibility of the consistence condition regarding an ML function generated by independent yet not identically distributed random variables. Numerical experiments justify our theoretical discoveries.

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

2012 ◽  
pp. 158-168
Author(s):  
Ying Zhou ◽  
Lizhi Wang
Keyword(s):  
Numerical Experiments ◽  
Proximal Point Algorithm ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
New Method ◽  
Proximal Method ◽  
Proximal Point ◽  
Nonlinear Complementarity ◽  
Correction Step

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

2010 ◽  
Vol 1 (3) ◽  
pp. 1-13
Author(s):  
Ying Zhou ◽  
Lizhi Wang
Keyword(s):  
Numerical Experiments ◽  
Proximal Point Algorithm ◽  
Complementarity Problems ◽  
Nonlinear Complementarity Problems ◽  
New Method ◽  
Proximal Method ◽  
Proximal Point ◽  
Nonlinear Complementarity ◽  
Correction Step

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

scholarly journals Efficient Computation of Highly Oscillatory Fourier Transforms with Nearly Singular Amplitudes over Rectangle Domains

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1930
Author(s):  
Zhen Yang ◽  
Junjie Ma
Keyword(s):  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Singular Integrals ◽  
Fourier Transforms ◽  
Adaptive Mesh ◽  
Oscillatory Integrals ◽  
Efficient Computation ◽  
New Approach ◽  
Highly Oscillatory ◽  
Nearly Singular Integrals

In this paper, we consider fast and high-order algorithms for calculation of highly oscillatory and nearly singular integrals. Based on operators with regard to Chebyshev polynomials, we propose a class of spectral efficient Levin quadrature for oscillatory integrals over rectangle domains, and give detailed convergence analysis. Furthermore, with the help of adaptive mesh refinement, we are able to develop an efficient algorithm to compute highly oscillatory and nearly singular integrals. In contrast to existing methods, approximations derived from the new approach do not suffer from high oscillatory and singularity. Finally, several numerical experiments are included to illustrate the performance of given quadrature rules.

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