scholarly journals Computing Exponential for Iterative Splitting Methods: Algorithms and Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-27 ◽  
Author(s):  
Jürgen Geiser
Keyword(s):  
Splitting Method ◽  
Real Life ◽  
Higher Order ◽  
Splitting Methods ◽  
Matrix Exponential ◽  
Approximation Schemes ◽  
Theoretical Point ◽  
Splitting Scheme ◽  
Splitting Schemes ◽  
Practical Applications

Iterative splitting methods have a huge amount to compute matrix exponential. Here, the acceleration and recovering of higher-order schemes can be achieved. From a theoretical point of view, iterative splitting methods are at least alternating Picards fix-point iteration schemes. For practical applications, it is important to compute very fast matrix exponentials. In this paper, we concentrate on developing fast algorithms to solve the iterative splitting scheme. First, we reformulate the iterative splitting scheme into an integral notation of matrix exponential. In this notation, we consider fast approximation schemes to the integral formulations, also known as -functions. Second, the error analysis is explained and applied to the integral formulations. The novelty is to compute cheaply the decoupled exp-matrices and apply only cheap matrix-vector multiplications for the higher-order terms. In general, we discuss an elegant way of embedding recently survey on methods for computing matrix exponential with respect to iterative splitting schemes. We present numerical benchmark examples, that compared standard splitting schemes with the higher-order iterative schemes. A real-life application in contaminant transport as a two phase model is discussed and the fast computations of the operator splitting method is explained.

A Splitting method for the calculation of the matrix exponential

Analysis ◽  
1994 ◽  
Vol 14 (2-3) ◽  
pp. 103-112 ◽  
Author(s):  
Eberhard U. Stichel
Keyword(s):  
Splitting Method ◽  
Matrix Exponential ◽  
The Matrix

Feature Subspace Estimation for Resolving Dimensionality Mismatch in Practical Color-Based Face Recognition Systems

2016 ◽  
Vol 30 (04) ◽  
pp. 1656004 ◽  
Author(s):  
Jae Young Choi
Keyword(s):  
Face Recognition ◽  
Color Image ◽  
Recognition Performance ◽  
Real Life ◽  
Practical Applications ◽  
Novel Approach ◽  
Feature Subspace ◽  
New Feature ◽  
Different Color ◽  
Input Level

Recently, considerable research efforts have been devoted to effective utilization of facial color information for improved recognition performance. Of all color-based face recognition (FR) methods, the most widely used approach is a color FR method using input-level fusion. In this method, augmented input vectors of the color images are first generated by concatenating different color components (including both luminance and chrominance information) by column order at the input level and feature subspace is then trained with a set of augmented input vectors. However, in practical applications, a testing image could be captured as a grayscale image, rather than as a color image, mainly caused by different, heterogeneous image acquisition environment. A grayscale testing image causes so-called dimensionality mismatch between the trained feature subspace and testing input vector. Disparity in dimensionality negatively impacts the reliable FR performance and even imposes a significant restriction on carrying out FR operations in practical color FR systems. To resolve the dimensionality mismatch, we propose a novel approach to estimate new feature subspace, suitable for recognizing a grayscale testing image. In particular, new feature subspace is estimated from a given feature subspace created using color training images. The effectiveness of proposed solution has been successfully tested on four public face databases (DBs) such as CMU, FERET, XM2VTSDB, and ORL DBs. Extensive and comparative experiments showed that the proposed solution works well for resolving dimensionality mismatch of importance in real-life color FR systems.

3D Printing Applications in STEM Education

2018 ◽  
pp. 2626-2640
Author(s):  
Norman Gwangwava ◽  
Catherine Hlahla
Keyword(s):  
3D Printing ◽  
Real Life ◽  
Printing Technology ◽  
Web Based ◽  
Practical Applications ◽  
3D Printing Technology ◽  
Lecture Room ◽  
Storage Products ◽  
Educational Toys ◽  
Learning Institutions

Using 3D printing technology in learning institutions brings an industrial experience to learners as well as an exposure to the same cutting-edge technologies encountered in real life careers. The chapter explores 3D printing technology at kindergarten (preschool), in the lecture room (BEng programme), and ready-to-use 3D printed products. In educational toy applications, the effect of poor product designs that do not meet the children's dimensional and safety requirements can lead to injuries, development of musculoskeletal disorders and health problems, some of which may be experienced by the children when they grow up. In order to address the problem of poor design, measurements of anthropometric dimensions from male and female children, aging from 6 to 7 years old were taken and concepts for educational toys were then generated. Other practical applications of the 3D printing technology explored in the chapter are lecture room demonstrations, prototyping of design projects and a web-based mass-customization of office mini-storage products.

Fifty years of Electronic Hardware Implementations of First and Higher Order Neural Networks

2010 ◽  
pp. 269-285 ◽  
Author(s):  
David R. Selviah ◽  
Janti Shawash
Keyword(s):  
Neural Networks ◽  
Real Time ◽  
High Speed ◽  
Higher Order ◽  
Low Latency ◽  
Real Time Control ◽  
Practical Applications ◽  
Field Programmable ◽  
On Chip ◽  
Electronic Hardware

This chapter celebrates 50 years of first and higher order neural network (HONN) implementations in terms of the physical layout and structure of electronic hardware, which offers high speed, low latency, compact, low cost, low power, mass produced systems. Low latency is essential for practical applications in real time control for which software implementations running on CPUs are too slow. The literature review chapter traces the chronological development of electronic neural networks (ENN) discussing selected papers in detail from analog electronic hardware, through probabilistic RAM, generalizing RAM, custom silicon Very Large Scale Integrated (VLSI) circuit, Neuromorphic chips, pulse stream interconnected neurons to Application Specific Integrated circuits (ASICs) and Zero Instruction Set Chips (ZISCs). Reconfigurable Field Programmable Gate Arrays (FPGAs) are given particular attention as the most recent generation incorporate Digital Signal Processing (DSP) units to provide full System on Chip (SoC) capability offering the possibility of real-time, on-line and on-chip learning.

Problem-Based Learning (PBL)

2021 ◽  
pp. 38-56
Author(s):  
Mahmoud Hawamdeh ◽  
Idris Adamu
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Real Life ◽  
Problem Based Learning ◽  
Higher Order ◽  
Educational Institutions ◽  
Learning Skills ◽  
Knowledge And Skills ◽  
Life Problems ◽  
Approach To Teaching

This chapter discuss how Problem-Based learning (PBL) helps to achieve this century's approach to teaching and learning for students in higher educational institutions. If adopted, this method of teaching will enable student to attain learning skills (skills, abilities, problem solving, and learning dispositions that have been identified) to acquire a lifelong habit of approaching problems with initiative and diligence and a drive to acquire the knowledge and skills needed for an effective resolution. And they will develop a systematic approach to solving real-life problems using higher-order skills.

An AI Walk from Pharmacokinetics to Marketing

2011 ◽  
pp. 71-75
Author(s):  
José D. Martín-Guerrero ◽  
Emilio Soria-Olivas ◽  
Paulo J.G. Lisboa ◽  
Antonio J. Serrano-López
Keyword(s):  
Finite Impulse Response ◽  
Clustering Algorithms ◽  
Real Life ◽  
Support Vector ◽  
Conditional Heteroskedasticity ◽  
Resonance Theory ◽  
Adaptive Resonance ◽  
Practical Applications ◽  
Life Problems ◽  
Auto Regressive

This work is intended for providing a review of reallife practical applications of Artificial Intelligence (AI) methods. We focus on the use of Machine Learning (ML) methods applied to rather real problems than synthetic problems with standard and controlled environment. In particular, we will describe the following problems in next sections: • Optimization of Erythropoietin (EPO) dosages in anaemic patients undergoing Chronic Renal Failure (CRF). • Optimization of a recommender system for citizen web portal users. • Optimization of a marketing campaign. The choice of these problems is due to their relevance and their heterogeneity. This heterogeneity shows the capabilities and versatility of ML methods to solve real-life problems in very different fields of knowledge. The following methods will be mentioned during this work: • Artificial Neural Networks (ANNs): Multilayer Perceptron (MLP), Finite Impulse Response (FIR) Neural Network, Elman Network, Self-Oganizing Maps (SOMs) and Adaptive Resonance Theory (ART). • Other clustering algorithms: K-Means, Expectation- Maximization (EM) algorithm, Fuzzy C-Means (FCM), Hierarchical Clustering Algorithms (HCA). • Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH). • Support Vector Regression (SVR). • Collaborative filtering techniques. • Reinforcement Learning (RL) methods.

scholarly journals Embedded Zassenhaus Expansion to Splitting Schemes: Theory and Multiphysics Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jürgen Geiser
Keyword(s):  
Fluid Dynamics ◽  
Convergence Rates ◽  
Operator Splitting ◽  
Main Idea ◽  
Computation Time ◽  
Product Formula ◽  
Splitting Methods ◽  
Splitting Schemes ◽  
Operator Splitting Methods ◽  
Multiphysics Problems

We present some operator splitting methods improved by the use of the Zassenhaus product and designed for applications to multiphysics problems. We treat iterative splitting methods that can be improved by means of the Zassenhaus product formula, which is a sequential splitting scheme. The main idea for reducing the computation time needed by the iterative scheme is to embed fast and cheap Zassenhaus product schemes, since the computation of the commutators involved is very cheap, since we are dealing with nilpotent matrices. We discuss the coupling ideas of iterative and sequential splitting techniques and their convergence. While the iterative splitting schemes converge slowly in their first iterative steps, we improve the initial convergence rates by embedding the Zassenhaus product formula. The applications are to multiphysics problems in fluid dynamics. We consider phase models in computational fluid dynamics and analyse how to obtain higher order operator splitting methods based on the Zassenhaus product. The computational benefits derive from the use of sparse matrices, which arise from the spatial discretisation of the underlying partial differential equations. Since the Zassenhaus formula requires nearly constant CPU time due to its sparse commutators, we have accelerated the iterative splitting schemes.

scholarly journals Weisfeiler and Leman Go Neural: Higher-Order Graph Neural Networks

2019 ◽  
Vol 33 ◽  
pp. 4602-4609 ◽  
Author(s):  
Christopher Morris ◽  
Martin Ritzert ◽  
Matthias Fey ◽  
William L. Hamilton ◽  
Jan Eric Lenssen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Multiple Scales ◽  
Graph Isomorphism ◽  
Higher Order ◽  
Point Of View ◽  
Theoretical Point ◽  
Graph Classification ◽  
Graph Neural Networks ◽  
Vector Representations

In recent years, graph neural networks (GNNs) have emerged as a powerful neural architecture to learn vector representations of nodes and graphs in a supervised, end-to-end fashion. Up to now, GNNs have only been evaluated empirically—showing promising results. The following work investigates GNNs from a theoretical point of view and relates them to the 1-dimensional Weisfeiler-Leman graph isomorphism heuristic (1-WL). We show that GNNs have the same expressiveness as the 1-WL in terms of distinguishing non-isomorphic (sub-)graphs. Hence, both algorithms also have the same shortcomings. Based on this, we propose a generalization of GNNs, so-called k-dimensional GNNs (k-GNNs), which can take higher-order graph structures at multiple scales into account. These higher-order structures play an essential role in the characterization of social networks and molecule graphs. Our experimental evaluation confirms our theoretical findings as well as confirms that higher-order information is useful in the task of graph classification and regression.

scholarly journals Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 156 ◽  
Author(s):  
Chanjuan Pan ◽  
Yuanheng Wang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Minimization Problem ◽  
Numerical Experiments ◽  
Splitting Method ◽  
Splitting Methods ◽  
Strong Convergence Theorem ◽  
Accretive Operators ◽  
Convex Minimization Problem ◽  
Inertial Extrapolation

In this article, we study a modified viscosity splitting method combined with inertial extrapolation for accretive operators in Banach spaces and then establish a strong convergence theorem for such iterations under some suitable assumptions on the sequences of parameters. As an application, we extend our main results to solve the convex minimization problem. Moreover, the numerical experiments are presented to support the feasibility and efficiency of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document