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 課程名稱 數值線性代數NUMERICAL LINEAR ALGEBRA 開課學期 99-1 授課對象 理學院  數學系 授課教師 林文偉 課號 MATH5411 課程識別碼 221 U4210 班次 學分 3 全/半年 半年 必/選修 選修 上課時間 星期一7,8,9(14:20~17:20) 上課地點 新304 備註 總人數上限：50人 Ceiba 課程網頁 http://ceiba.ntu.edu.tw/991nla 課程簡介影片 核心能力關聯 本課程尚未建立核心能力關連 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 I ON THE NUMERICAL SOLUTIONS OF LINEAR SYSTEMS 1. INTRODUCTION ．Mathematical Auxiliary, Definitions and Relations ．Norms and Eigenvalues ．The Sensitivity of Linear System AX = B 2. NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS ．Elementary matrices ．LR-Factorization ．Gaussian Elimination ．Special linear System 3. ORTHOGONALIZATION AND LEAST SQUARES METHODS ．QR-Factorization (QR-Decomposition) ．Overdetermined Linear Systems - Least Squares methods 4. ITERATIVE METHODS FOR SOLVING LARGE LINEAR SYSTEMS ．General procedures for the Construction of Iterative Methods ．Relaxation Methods (Successive Over-Relaxation (SOR) Method ) ．Application to Finite Difference Methods: Model Problem (Example 4.1.3) ．Block Iterative Methods ．The ADI Method of Peaceman and Rachford ．Derivation and Properties of the Conjugate Gradient Method ．CG-Method as an Iterative Method, Preconditioning ．Incomplete Cholesky Decomposition ．Chebychev Semi-Iteration Acceleration Method ．GCG-Type Methods for Nonsymmetric Linear Systems ．CGS (Conjugate Gradient Squared), a Fast Lanczos-Type Solver for Nonsymmetric Linear Systems ．BI-CGSTAB: A fast and Smoothly Converging Variant of BI-CG for the Solution of Nonsymmetric Linear Systems ．A Transpose-Free Qusi-Minimal Residual Algorithm for Nonsymmetric Linear Systems ．GMRES: Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems II ON THE NUMERICAL SOLUTIONS OF EIGENVALUE PROBLEMS 5. THE UNSYMMETRIC EIGENVALUE PROBLEM ．Orthogonal Projections and C-S Decomposition ．Perturbation Theory ．Power Iterations ．QR-Algorithm (QR-Method, QR-Iteration) ．LR, LRC AND QR Algorithms for Positive Definite Matrices ．QD-Algorithm (Quotient Difference) 課程目標 課程要求 預期每週課後學習時數 Office Hours 指定閱讀 參考書目 (1) B. N. Datta. Numerical Linear Algebra and Applications, Cole Publishing Company, Pacific Grove, California, 2nd ed., 2010. (2) G. H. Golub and C. F. Van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore, 3rd ed., 1996. (3) D. S. Watkins, Fundamentals of matrix computations, John Wiley and Sons, 3rd ed., 2010 評量方式(僅供參考)
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