scholarly journals Family of simultaneous methods with corrections for approximating zeros of analytic functions

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2217-2225
Author(s):  
Lidija Rancic
Keyword(s):  
Analytic Functions ◽  
Computational Cost ◽  
Convergence Properties ◽  
Simultaneous Methods ◽  
Good Convergence ◽  
Basic Family ◽  
Complex Zeros ◽  
Low Computational Cost ◽  
Theoretical Results ◽  
Methods Numerical

A family of accelerated iterative methods for the simultaneous approximation of complex zeros of a class of analytic functions is proposed. Considered analytic functions have only simple zeros inside a simple smooth closed contour in the complex plane. It is shown that the order of convergence of the basic family can be increased from four to five and six using Newton?s and Halley?s corrections, respectively. The improved convergence is achieved on the account of additional calculations of low computational cost, which significantly increases the computational efficiency of the accelerated methods. Numerical examples demonstrate a good convergence properties, fitting very well theoretical results.

scholarly journals ISOGEOMETRIC COLLOCATION METHODS

2010 ◽  
Vol 20 (11) ◽  
pp. 2075-2107 ◽  
Author(s):  
F. AURICCHIO ◽  
L. BEIRÃO DA VEIGA ◽  
T. J. R. HUGHES ◽  
A. REALI ◽  
G. SANGALLI
Keyword(s):  
Theoretical Analysis ◽  
Isogeometric Analysis ◽  
Computational Cost ◽  
Basis Functions ◽  
Three Dimensions ◽  
Collocation Methods ◽  
One Dimensional ◽  
Numerical Tests ◽  
Low Computational Cost ◽  
Theoretical Results

We initiate the study of collocation methods for NURBS-based isogeometric analysis. The idea is to connect the superior accuracy and smoothness of NURBS basis functions with the low computational cost of collocation. We develop a one-dimensional theoretical analysis, and perform numerical tests in one, two and three dimensions. The numerical results obtained confirm theoretical results and illustrate the potential of the methodology.

scholarly journals Computer tools for the construction and analysis of some efficient root-finding simultaneous methods

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2151-2169
Author(s):  
Ivan Petkovic ◽  
Djordje Herceg
Keyword(s):  
High Efficiency ◽  
Algebraic Polynomials ◽  
Convergence Properties ◽  
Simultaneous Methods ◽  
Computer Tools ◽  
Root Finding ◽  
Accelerated Methods ◽  
The Stability ◽  
Additional Arithmetic ◽  
Complex Zeros

Using the tools provided by computer algebra system Mathematica, we consider two iterative methods of high efficiency for the simultaneous approximation of simple or multiple (real or complex) zeros of algebraic polynomials. The proposed methods are based on the fourth-order Schr?der-like methods of the first and second kind. We prove that the order of convergence of both basic total-step simultaneous methods is equal to five. Using corrective approximations produced by methods of order two, three and four for finding a single multiple zero, the convergence order is increased from five to six, seven, and eight, respectively. The increased convergence speed is attained with negligible number of additional arithmetic operations, which significantly increases the computational efficiency of the accelerated methods. Convergence properties of the proposed methods are demonstrated by numerical examples and graphics visualization by plotting trajectories of zero approximations. Flows of iterative processes, presented by these trajectories, point to the stability and robustness of the proposed methods.

scholarly journals Computing Expectiles Using k-Nearest Neighbours Approach

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 645
Author(s):  
Muhammad Farooq ◽  
Sehrish Sarfraz ◽  
Christophe Chesneau ◽  
Mahmood Ul Hassan ◽  
Muhammad Ali Raza ◽  
...  
Keyword(s):  
Computational Cost ◽  
Real Life ◽  
Distance Measures ◽  
Computational Time ◽  
High Dimensional ◽  
Test Error ◽  
Nearest Neighbours ◽  
Comparable Performance ◽  
Asymmetric Least Squares ◽  
Low Computational Cost

Expectiles have gained considerable attention in recent years due to wide applications in many areas. In this study, the k-nearest neighbours approach, together with the asymmetric least squares loss function, called ex-kNN, is proposed for computing expectiles. Firstly, the effect of various distance measures on ex-kNN in terms of test error and computational time is evaluated. It is found that Canberra, Lorentzian, and Soergel distance measures lead to minimum test error, whereas Euclidean, Canberra, and Average of (L1,L∞) lead to a low computational cost. Secondly, the performance of ex-kNN is compared with existing packages er-boost and ex-svm for computing expectiles that are based on nine real life examples. Depending on the nature of data, the ex-kNN showed two to 10 times better performance than er-boost and comparable performance with ex-svm regarding test error. Computationally, the ex-kNN is found two to five times faster than ex-svm and much faster than er-boost, particularly, in the case of high dimensional data.

scholarly journals Directional TGV-Based Image Restoration under Poisson Noise

2021 ◽  
Vol 7 (6) ◽  
pp. 99
Author(s):  
Daniela di Serafino ◽  
Germana Landi ◽  
Marco Viola
Keyword(s):  
Computed Tomography ◽  
Image Restoration ◽  
Gaussian Noise ◽  
Computational Cost ◽  
Data Fitting ◽  
Poisson Noise ◽  
Glass Fibres ◽  
Leibler Divergence ◽  
Generalized Variation ◽  
Low Computational Cost

We are interested in the restoration of noisy and blurry images where the texture mainly follows a single direction (i.e., directional images). Problems of this type arise, for example, in microscopy or computed tomography for carbon or glass fibres. In order to deal with these problems, the Directional Total Generalized Variation (DTGV) was developed by Kongskov et al. in 2017 and 2019, in the case of impulse and Gaussian noise. In this article we focus on images corrupted by Poisson noise, extending the DTGV regularization to image restoration models where the data fitting term is the generalized Kullback–Leibler divergence. We also propose a technique for the identification of the main texture direction, which improves upon the techniques used in the aforementioned work about DTGV. We solve the problem by an ADMM algorithm with proven convergence and subproblems that can be solved exactly at a low computational cost. Numerical results on both phantom and real images demonstrate the effectiveness of our approach.

scholarly journals An optimal and low computational cost fractional Newton-type method for solving nonlinear equations

2021 ◽  
pp. 107650
Author(s):  
Giro Candelario ◽  
Alicia Cordero ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Nonlinear Equations ◽  
Computational Cost ◽  
Type Method ◽  
Low Computational Cost

Low-Computational Cost Estimation Algorithm for Adaptive Optics Systems*

2011 ◽  
Vol 44 (1) ◽  
pp. 5573-5578
Author(s):  
M. Abbas Turki ◽  
D. Esqueda Merino ◽  
K. Kasper ◽  
C. Durieu
Keyword(s):  
Adaptive Optics ◽  
Cost Estimation ◽  
Computational Cost ◽  
Estimation Algorithm ◽  
Low Computational Cost

scholarly journals Status Estimation and In-Process Connection of Kanbans Using BLE Beacons and LPWA Network to Implement Intra-Traceability for the Kanban System

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5038
Author(s):  
Kosuke Shima ◽  
Masahiro Yamaguchi ◽  
Takumi Yoshida ◽  
Takanobu Otsuka
Keyword(s):  
Inventory Management ◽  
Low Cost ◽  
Computational Cost ◽  
Low Energy ◽  
Manufacturing Strategy ◽  
Implementation Cost ◽  
Measurement Systems ◽  
Process Route ◽  
Kanban System ◽  
Low Computational Cost

IoT-based measurement systems for manufacturing have been widely implemented. As components that can be implemented at low cost, BLE beacons have been used in several systems developed in previous research. In this work, we focus on the Kanban system, which is a measure used in manufacturing strategy. The Kanban system emphasizes inventory management and is used to produce only required amounts. In the Kanban system, the Kanban cards are rotated through the factory along with the products, and when the products change to a different process route, the Kanban card is removed from the products and the products are assigned to another Kanban. For this reason, a single Kanban cannot trace products from plan to completion. In this work, we propose a system that uses a Bluetooth low energy (BLE) beacon to connect Kanbans in different routes but assigned to the same products. The proposed method estimates the beacon status of whether the Kanban is inside or outside a postbox, which can then be computed by a micro controller at low computational cost. In addition, the system connects the Kanbans using the beacons as paired connection targets. In an experiment, we confirmed that the system connected 70% of the beacons accurately. We also confirmed that the system could connect the Kanbans at a small implementation cost.

scholarly journals Fast Image Registration for Spacecraft Autonomous Navigation Using Natural Landmarks

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Yun-Hua Wu ◽  
Lin-Lin Ge ◽  
Feng Wang ◽  
Bing Hua ◽  
Zhi-Ming Chen ◽  
...  
Keyword(s):  
Image Registration ◽  
Autonomous Navigation ◽  
Computational Cost ◽  
Segmentation Algorithm ◽  
Speeded Up Robust Features ◽  
Speed Up ◽  
Random Sample Consensus ◽  
Invariant Properties ◽  
Low Computational Cost ◽  
Ransac Algorithm

In order to satisfy the real-time requirement of spacecraft autonomous navigation using natural landmarks, a novel algorithm called CSA-SURF (chessboard segmentation algorithm and speeded up robust features) is proposed to improve the speed without loss of repeatability performance of image registration progress. It is a combination of chessboard segmentation algorithm and SURF. Here, SURF is used to extract the features from satellite images because of its scale- and rotation-invariant properties and low computational cost. CSA is based on image segmentation technology, aiming to find representative blocks, which will be allocated to different tasks to speed up the image registration progress. To illustrate the advantages of the proposed algorithm, PCA-SURF, which is the combination of principle component analysis and SURF, is also analyzed in this paper for comparison. Furthermore, random sample consensus (RANSAC) algorithm is applied to eliminate the false matches for further accuracy improvement. The simulation results show that the proposed strategy obtains good results, especially in scaling and rotation variation. Besides, CSA-SURF decreased 50% of the time in extraction and 90% of the time in matching without losing the repeatability performance by comparing with SURF algorithm. The proposed method has been demonstrated as an alternative way for image registration of spacecraft autonomous navigation using natural landmarks.

On the Use of Symmetries in Building Surrogate Models

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
M. Giselle Fernández-Godino ◽  
S. Balachandar ◽  
Raphael T. Haftka
Keyword(s):  
Linear Regression ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Surrogate Models ◽  
Black Box ◽  
Basis Functions ◽  
Regression Kriging ◽  
Challenges And Opportunities ◽  
Designs Of Experiments ◽  
Low Computational Cost

When simulations are expensive and multiple realizations are necessary, as is the case in uncertainty propagation, statistical inference, and optimization, surrogate models can achieve accurate predictions at low computational cost. In this paper, we explore options for improving the accuracy of a surrogate if the modeled phenomenon presents symmetries. These symmetries allow us to obtain free information and, therefore, the possibility of more accurate predictions. We present an analytical example along with a physical example that has parametric symmetries. Although imposing parametric symmetries in surrogate models seems to be a trivial matter, there is not a single way to do it and, furthermore, the achieved accuracy might vary. We present four different ways of using symmetry in surrogate models. Three of them are straightforward, but the fourth is original and based on an optimization of the subset of points used. The performance of the options was compared with 100 random designs of experiments (DoEs) where symmetries were not imposed. We found that each of the options to include symmetries performed the best in one or more of the studied cases and, in all cases, the errors obtained imposing symmetries were substantially smaller than the worst cases among the 100. We explore the options for using symmetries in two surrogates that present different challenges and opportunities: Kriging and linear regression. Kriging is often used as a black box; therefore, we consider approaches to include the symmetries without changes in the main code. On the other hand, since linear regression is often built by the user; owing to its simplicity, we consider also approaches that modify the linear regression basis functions to impose the symmetries.

Sign in / Sign up

Export Citation Format

Share Document