102 research outputs found

    Global convergence of a new hybrid Gauss-Newton structured BFGS method for nonlinear least squares problems

    Get PDF
    2009-2010 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

    Arbitrary lagrangian-eulerian formulation of quasistatic nonlinear problems

    Get PDF
    En esta tesis se presenta una metodología para la simulación numérica de procesos cuasistaticos en mecánica de sólidos no lineal, basada en una formulación arbitrariamente lagrangiana-euleriana (ale) del problema. Se hace un enfoque generalista, que abarca algunas cuestiones fundamentales en mecánica computacional y en análisis numérico: la resolución de sistemas no lineales de ecuaciones algebraicas y la integración de las ecuaciones constitutivas no lineales. Como entorno de trabajo se utiliza un código orientado al objeto, una herramienta muy útil en tareas de investigación pues proporciona un lenguaje interactivo de programación altamente conceptual. Este lenguaje permite implementar y estudiar los algoritmos numéricos de manera sencilla y eficaz.Las principales aportaciones del trabajo son: (1) La adaptación de distintos métodos para la resolución de sistemas no lineales de ecuaciones a la técnica de los multiplicadores de lagrange: desarrollo de algoritmos, análisis de convergencia e implementación numérica.(2) El desarrollo de una estrategia para el análisis del orden del error de esquemas numéricos de integración de las ecuaciones constitutivas no lineales en mecánica de sólidos con grandes deformaciones, y la aplicación de dicha estrategia a dos algoritmos.(3) El tratamiento unificado de la formulación ale de problemas cuasistaticos y dinámicos(4) El desarrollo de algoritmos para el tratamiento de los términos conectivos en las ecuaciones constitutivas ale

    Single-channel source separation using non-negative matrix factorization

    Get PDF

    A survey on numerical methods for unconstrained optimization problems.

    Get PDF
    by Chung Shun Shing.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 158-170).Abstracts in English and Chinese.List of Figures --- p.xChapter 1 --- Introduction --- p.1Chapter 1.1 --- Background and Historical Development --- p.1Chapter 1.2 --- Practical Problems --- p.3Chapter 1.2.1 --- Statistics --- p.3Chapter 1.2.2 --- Aerodynamics --- p.4Chapter 1.2.3 --- Factory Allocation Problem --- p.5Chapter 1.2.4 --- Parameter Problem --- p.5Chapter 1.2.5 --- Chemical Engineering --- p.5Chapter 1.2.6 --- Operational Research --- p.6Chapter 1.2.7 --- Economics --- p.6Chapter 1.3 --- Mathematical Models for Optimization Problems --- p.6Chapter 1.4 --- Unconstrained Optimization Techniques --- p.8Chapter 1.4.1 --- Direct Method - Differential Calculus --- p.8Chapter 1.4.2 --- Iterative Methods --- p.10Chapter 1.5 --- Main Objectives of the Thesis --- p.11Chapter 2 --- Basic Concepts in Optimizations of Smooth Func- tions --- p.14Chapter 2.1 --- Notation --- p.14Chapter 2.2 --- Different Types of Minimizer --- p.16Chapter 2.3 --- Necessary and Sufficient Conditions for Optimality --- p.18Chapter 2.4 --- Quadratic Functions --- p.22Chapter 2.5 --- Convex Functions --- p.24Chapter 2.6 --- "Existence, Uniqueness and Stability of a Minimum" --- p.29Chapter 2.6.1 --- Existence of a Minimum --- p.29Chapter 2.6.2 --- Uniqueness of a Minimum --- p.30Chapter 2.6.3 --- Stability of a Minimum --- p.31Chapter 2.7 --- Types of Convergence --- p.34Chapter 2.8 --- Minimization of Functionals --- p.35Chapter 3 --- Steepest Descent Method --- p.37Chapter 3.1 --- Background --- p.37Chapter 3.2 --- Line Search Method and the Armijo Rule --- p.39Chapter 3.3 --- Steplength Control with Polynomial Models --- p.43Chapter 3.3.1 --- Quadratic Polynomial Model --- p.43Chapter 3.3.2 --- Safeguarding --- p.45Chapter 3.3.3 --- Cubic Polynomial Model --- p.46Chapter 3.3.4 --- General Line Search Strategy --- p.49Chapter 3.3.5 --- Algorithm of Steepest Descent Method --- p.51Chapter 3.4 --- Advantages of the Armijo Rule --- p.54Chapter 3.5 --- Convergence Analysis --- p.56Chapter 4 --- Iterative Methods Using Second Derivatives --- p.63Chapter 4.1 --- Background --- p.63Chapter 4.2 --- Newton's Method --- p.64Chapter 4.2.1 --- Basic Concepts --- p.64Chapter 4.2.2 --- Convergence Analysis of Newton's Method --- p.65Chapter 4.2.3 --- Newton's Method with Steplength --- p.69Chapter 4.2.4 --- Convergence Analysis of Newton's Method with Step-length --- p.70Chapter 4.3 --- Greenstadt's Method --- p.72Chapter 4.4 --- Marquardt-Levenberg Method --- p.74Chapter 4.5 --- Fiacco and McComick Method --- p.76Chapter 4.6 --- Matthews and Davies Method --- p.79Chapter 4.7 --- Numerically Stable Modified Newton's Method --- p.80Chapter 4.8 --- The Role of the Second Derivative Methods --- p.89Chapter 5 --- Multi-step Methods --- p.92Chapter 5.1 --- Background --- p.93Chapter 5.2 --- Heavy Ball Method --- p.94Chapter 5.3 --- Conjugate Gradient Method --- p.99Chapter 5.3.1 --- Some Types of Conjugate Gradient Method --- p.99Chapter 5.3.2 --- Convergence Analysis of Conjugate Gradient Method --- p.108Chapter 5.4 --- Methods of Variable Metric and Methods of Conju- gate Directions --- p.111Chapter 5.5 --- Other Approaches for Constructing the First-order Methods --- p.116Chapter 6 --- Quasi-Newton Methods --- p.121Chapter 6.1 --- Disadvantages of Newton's Method --- p.122Chapter 6.2 --- General Idea of Quasi-Newton Method --- p.124Chapter 6.2.1 --- Quasi-Newton Methods --- p.124Chapter 6.2.2 --- Convergence of Quasi-Newton Methods --- p.129Chapter 6.3 --- Properties of Quasi-Newton Methods --- p.131Chapter 6.4 --- Some Particular Algorithms for Quasi-Newton Methods --- p.137Chapter 6.4.1 --- Single-Rank Algorithms --- p.137Chapter 6.4.2 --- Double-Rank Algorithms --- p.144Chapter 6.4.3 --- Other Applications --- p.149Chapter 6.5 --- Conclusion --- p.152Chapter 7 --- Choice of Methods in Optimization Problems --- p.154Chapter 7.1 --- Choice of Methods --- p.154Chapter 7.2 --- Conclusion --- p.157Bibliography --- p.15
    corecore