Topic
Multidimensional systems
About: Multidimensional systems is a research topic. Over the lifetime, 2310 publications have been published within this topic receiving 82205 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: This paper analyzes a particle's trajectory as it moves in discrete time, then progresses to the view of it in continuous time, leading to a generalized model of the algorithm, containing a set of coefficients to control the system's convergence tendencies.
Abstract: The particle swarm is an algorithm for finding optimal regions of complex search spaces through the interaction of individuals in a population of particles. This paper analyzes a particle's trajectory as it moves in discrete time (the algebraic view), then progresses to the view of it in continuous time (the analytical view). A five-dimensional depiction is developed, which describes the system completely. These analyses lead to a generalized model of the algorithm, containing a set of coefficients to control the system's convergence tendencies. Some results of the particle swarm optimizer, implementing modifications derived from the analysis, suggest methods for altering the original algorithm in ways that eliminate problems and increase the ability of the particle swarm to find optima of some well-studied test functions.
9,397 citations
Book•
1 Jan 2002TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.
Abstract: Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.
7,179 citations
TL;DR: Using maximum entropy approximations of differential entropy, a family of new contrast (objective) functions for ICA enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions.
Abstract: Independent component analysis (ICA) is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible. We use a combination of two different approaches for linear ICA: Comon's information theoretic approach and the projection pursuit approach. Using maximum entropy approximations of differential entropy, we introduce a family of new contrast functions for ICA. These contrast functions enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions. The statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model, and it is shown how to choose contrast functions that are robust and/or of minimum variance. Finally, we introduce simple fixed-point algorithms for practical optimization of the contrast functions.
6,786 citations
TL;DR: The general regression neural network (GRNN) is a one-pass learning algorithm with a highly parallel structure that provides smooth transitions from one observed value to another.
Abstract: A memory-based network that provides estimates of continuous variables and converges to the underlying (linear or nonlinear) regression surface is described. The general regression neural network (GRNN) is a one-pass learning algorithm with a highly parallel structure. It is shown that, even with sparse data in a multidimensional measurement space, the algorithm provides smooth transitions from one observed value to another. The algorithmic form can be used for any regression problem in which an assumption of linearity is not justified. >
4,586 citations
Book•
27 Oct 2003TL;DR: In this paper, a simple bifurcation of a nonlinear problem multiple solutions of a Nonlinear Problem Nonlinear Eigenvalue Problem Thomas-Fermi Atom Model Volterra's Population Model Free Oscillation Systems with Odd Nonlinearity Free oscillations with Quadratic nonlinearity Limit Cycle in a Multidimensional System Blasius' viscous flow Boundary-layer Flow Boundarylayer Flow with Exponential Property Boundary Layer Flow with Algebraic Property Von Karman Swirling Flow Nonlinear Progressive Waves in Deep Water BIBLIOGR
Abstract: PART I BASIC IDEAS Introduction Illustrative Description Systematic Description Relations to Some Previous Analytic Methods Advantages, Limitations, and Open Questions PART II APPLICATIONS Simple Bifurcation of a Nonlinear Problem Multiple Solutions of a Nonlinear Problem Nonlinear Eigenvalue Problem Thomas-Fermi Atom Model Volterra's Population Model Free Oscillation Systems with Odd Nonlinearity Free Oscillation Systems with Quadratic Nonlinearity Limit Cycle in a Multidimensional System Blasius' viscous Flow Boundary-layer Flow with Exponential Property Boundary-layer Flow with Algebraic Property Von Karman Swirling Flow Nonlinear Progressive Waves in Deep Water BIBLIOGRAPHY INDEX
3,173 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 5 |
| 2023 | 10 |
| 2022 | 6 |
| 2021 | 16 |
| 2020 | 40 |