scholarly journals Reducing the Computational Complexity for BLAST by Using a Novel Fast Algorithm to Compute an Initial Square-Root Matrix

2008 ◽  
Author(s):  
Hufei Zhu ◽  
Wen Chen ◽  
Dageng Chen ◽  
Yinggang Du ◽  
Jianmin Lu
Keyword(s):  
Computational Complexity ◽  
Fast Algorithm ◽  
Square Root

Fast algorithm for the three-dimensional Poisson equation in infinite domains

2020 ◽  
Author(s):  
Chunxiong Zheng ◽  
Xiang Ma
Keyword(s):  
Poisson Equation ◽  
Fast Algorithm ◽  
Root Function ◽  
Computational Cost ◽  
Three Dimensional ◽  
Chebyshev Approximation ◽  
Laplacian Operator ◽  
Square Root ◽  
Infinite Domain ◽  
Infinite Domains

Abstract This paper is concerned with a fast finite element method for the three-dimensional Poisson equation in infinite domains. Both the exterior problem and the strip-tail problem are considered. Exact Dirichlet-to-Neumann (DtN)-type artificial boundary conditions (ABCs) are derived to reduce the original infinite-domain problems to suitable truncated-domain problems. Based on the best relative Chebyshev approximation for the square-root function, a fast algorithm is developed to approximate exact ABCs. One remarkable advantage is that one need not compute the full eigensystem associated with the surface Laplacian operator on artificial boundaries. In addition, compared with the modal expansion method and the method based on Pad$\acute{\textrm{e}}$ approximation for the square-root function, the computational cost of the DtN mapping is further reduced. An error analysis is performed and numerical examples are presented to demonstrate the efficiency of the proposed method.

scholarly journals The Square Root UKF-SLAM Algorithm Based on the Smallest Proportion of Skewness in Single Line Sampling

2018 ◽  
Vol 160 ◽  
pp. 06005
Author(s):  
MengYuan Chen ◽  
GuoWei Qin ◽  
Tong Xu
Keyword(s):  
Computational Complexity ◽  
Covariance Matrix ◽  
Sampling Strategy ◽  
Single Line ◽  
Estimation Accuracy ◽  
Square Root ◽  
Line Sampling ◽  
Algorithm Stability ◽  
Slam Algorithm ◽  
Symmetric Sampling

In view of the distortion in the filter gain matrix calculation as well as the high computational complexity and the nonlocal effect of symmetric sampling that exists in the UKF-SLAM algorithm, the square root UKF-SLAM algorithm based on the smallest proportion of skewness in single line sampling was proposed. According to the mended algorithm, the square root of covariance matrix is brought into iteration operation instead of covariance matrix, moreover, the smallest proportion of skewness in single line sampling is utilized for the optimization of sampling strategy. The results of simulation show that the algorithm can effectively improve the position accuracy in robot as well as the estimation accuracy of feature map. Furthermore, the computational complexity is reduced and the algorithm stability is improved.

A fast algorithm for sparse multichannel blind deconvolution

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. V7-V16 ◽  
Author(s):  
Kenji Nose-Filho ◽  
André K. Takahata ◽  
Renato Lopes ◽  
João M. T. Romano
Keyword(s):  
Computational Complexity ◽  
Loss Function ◽  
Fast Algorithm ◽  
Blind Deconvolution ◽  
Synthetic Data ◽  
Minimum Entropy ◽  
Data Set ◽  
Robust Solution ◽  
Marine Data ◽  
The One

We have addressed blind deconvolution in a multichannel framework. Recently, a robust solution to this problem based on a Bayesian approach called sparse multichannel blind deconvolution (SMBD) was proposed in the literature with interesting results. However, its computational complexity can be high. We have proposed a fast algorithm based on the minimum entropy deconvolution, which is considerably less expensive. We designed the deconvolution filter to minimize a normalized version of the hybrid [Formula: see text]-norm loss function. This is in contrast to the SMBD, in which the hybrid [Formula: see text]-norm function is used as a regularization term to directly determine the deconvolved signal. Results with synthetic data determined that the performance of the obtained deconvolution filter was similar to the one obtained in a supervised framework. Similar results were also obtained in a real marine data set for both techniques.

Fast algorithm for calculating autocorrelation function in code synthesis tasks by enumerative technique

2021 ◽  
Vol 1 (1) ◽  
pp. 13-18
Author(s):  
A. V. Korobeinikov
Keyword(s):  
Computational Complexity ◽  
Autocorrelation Function ◽  
Linear Dependence ◽  
Fast Algorithm ◽  
Binary Code ◽  
Code Combination ◽  
Current Code

The fast algorithm for calculating the autocorrelation function (ACF) of a binary code is developed in relation to the problem of synthesizing codes with a given ACF by enumerative technique. The algorithm is applicable for any duration of the N code. The computational complexity of calculating the ACF is 2N multiplication operations and 2N addition operations. The linear dependence of computational complexity on the duration of the N code is noted. To calculate the ACF of the newly created code combination, the previous code, its ACF, and the index of the changed code element are used. The condition of applicability of the algorithm is that the search of code combinations must be performed by changing only one element in the current code combination. An enumerative technique is proposed that allows a complete enumertion of all 2N existing combinations by sequentially changing the code combination of just one element.

scholarly journals FAST STEREO IMAGE DEPTH ESTIMATION ALGORITHM BASED ON CHANGE DETECTION METHODS IN CAMERAS FIELD OF VIEW

2018 ◽  
pp. 94-98
Author(s):  
A. V. Khamukhin ◽  
V. V. Kuzmina
Keyword(s):  
Computational Complexity ◽  
Fast Algorithm ◽  
Moving Objects ◽  
Depth Estimation ◽  
Estimation Algorithm ◽  
Video Stream ◽  
Field Of View ◽  
Stereo Image ◽  
Detection Methods ◽  
Image Depth

Stereo image depth estimation algorithms have not been widely used in CCTV systems yet, since either their accuracy is low or their computational complexity is high, which prevents implementation of these algorithms due to economic limitations on the cost of equipment used in security systems. In this paper, a new fast algorithm is proposed for reconstructing the depth of stereo images, which is used for reliable event identification in the CCTV systems cameras field of view. This real-time video stream processing method is based on the use of a fast algorithm for detecting changes in the cameras scene in the combination with SGBM depth estimation algorithm, which processes only image areas containing scene changes. The proposed method of significant computational complexity reduction of the depth estimation algorithm makes possible to acquire information about the distance from the cameras to moving objects in the field of view and use this information as an additional feature, that helps to reduce the operational cost and to improve the reliability of CCTV systems.

A Fast Algorithm for Vector ARMA Parameter Estimation

2012 ◽  
Vol 433-440 ◽  
pp. 4475-4481
Author(s):  
Zhi Qing Chen ◽  
You Shen Xia
Keyword(s):  
Parameter Estimation ◽  
Computational Complexity ◽  
Fast Algorithm ◽  
Linear Equations ◽  
Estimation Problem ◽  
Parameter Estimation Problem ◽  
Model Technique

In this paper, a fast algorithm for vector autoregressivemoving-average (ARMA) parameter estimation under noise environments is proposed. Based on an equivalent AR parameter model technique and a Yule-Walker equation technique, solving the parameter estimation problem of the VARMA model is well converted into solving linear equations. Therefore, the proposed algorithm has a lower computational complexity and a faster speed than conventional algorithms. Application examples with application to Lorenz systems confirm that the proposed algorithm can obtain a good solution.

A fast algorithm for group square-root Lasso based group-sparse regression

2021 ◽  
pp. 108142
Author(s):  
Chunlei Zhao ◽  
Xingpeng Mao ◽  
Minqiu Chen ◽  
Changjun Yu
Keyword(s):  
Fast Algorithm ◽  
Square Root ◽  
Sparse Regression

scholarly journals An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
F. Soleymani ◽  
M. Sharifi ◽  
S. Shateyi ◽  
F. Khaksar Haghani
Keyword(s):  
Fast Algorithm ◽  
Computational Algorithm ◽  
Geometric Mean ◽  
Positive Definite ◽  
Convergence Order ◽  
Square Root ◽  
Positive Definite Matrices ◽  
Matrix Square Root

Using the relation between a principal matrix square root and its inverse with the geometric mean, we present a fast algorithm for computing the geometric mean of two Hermitian positive definite matrices. The algorithm is stable and possesses a high convergence order. Some experiments are included to support the proposed computational algorithm.

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