授業科目名 年度 学期 開講曜日・時限 学部・研究科 全担当教員 単位数
35260:Numerical Algorithms(G1) 2019 秋セメスター 月5 情報理工学部 白 楊 2

キャンパス

BKC

授業施設

フォレストハウス１０２号教室

授業で利用する言語

英語

授業の概要と方法

This course brings an introduction to the numerical analysis. The goal of the course is to develop a basic understanding of numerical algorithms, as well as to train skills for selecting and applying feasible algorithms in solving “real world” problems. Specifically, this course covers numerical root finding problems, interpolation and approximation problems, numerical differentiation and integration, as well as problems of solving a system of equations numerically, and so on.

受講生の到達目標

After this course, students will be able to understand the principle that how computers are dealing with mathematical problems, such as solving differentiation and integration problems, differential equations, and optimization problems. Also, they will learn the basic terms in numerical mathematics and the techniques for the analysis of numerical algorithms. Based on these techniques, students are expected to be able to solve concrete problems by selecting or even devising feasible algorithms.

事前に履修しておくことが望まれる科目

Calculus, Linear Algebra, basic programming skills

授業スケジュール

授業回数/
担当教員（複数担当の場合） 		テーマ
キーワード・文献・補足事項等
1

Preliminaries of Computing

Basic concepts: round-off errors, floating point arithmetic, convergence
2

Root Finding

Bisection method, fixed-point iteration, Newton’s method, error analysis for iterative methods
3

Interpolation

Lagrange polynomial, divided differences, Hermite interpolation
4

Numerical Differentiation and Integration (1)

Numerical differentiation: Richardson’s extrapolation, etc.
5

Numerical Differentiation and Integration (2)

Numerical integration: Trapezoidal rule, etc., Gaussian quadrature and Euler-Maclaurin formula
6

Numerical Solutions to System of Equations (1)

Direct methods for solving linear systems of equations: pivoting strategies, Linear Algebra and Matrix Inversion
7

Numerical Solutions to System of Equations (2)

Iterative methods for solving linear systems of equations: Jacobi and Gauss-Siedel iterative techniques, etc.
8

Numerical Solutions to System of Equations (3)

Solving nonlinear systems of equations: fixed points for functions of several variables, Newton’s method
9

Mid-term Exam

Lasts 90 min. and covers topics of Weeks 1 through 8
10

Solving Differential Equations (1)

IVP problems for ODE: Euler’s, Taylor, Runge-Kutta, and multistep methods, stability
11

Solving Differential Equations (2)

BVP problems for ODE: shooting methods, finite-difference methods
12

Solving Differential Equations (3)

Partial Differential Equations: an introduction to the finite-element method
13

Approximation Theory (1)

Orthogonal polynomials and least Squares approximation, Chebyshev polynomials
14

Approximation Theory (2)

Approximating Eigenvalues: Power method, Householder’s method
15

Course Overview

Covers topics of Weeks 1 through 14

授業実施形態

授業外学習の指示

Students are recommended to read relevant chapters before class. This will be helpful for them to better and faster understand the contents of the lecture. Homework will be assigned within each lecture and is due on the next lecture. Collaboration on homework is encouraged because discussion with other students is an efficient way of solving challenging problems. However, it is not allowed to copy solutions from other students directly.

成績評価方法

種別 割合(%) 評価基準等
定期試験（筆記） 50

Ability to solve the questions provided in the final exam
レポート試験
（統一締切日を締切とするレポート）

上記以外の試験・レポート、平常点評価
（日常的な授業における取組状況の評価）		 50

Attendance, assignments and the mid-term exam

成績評価方法(備考)

Algorithms involving matrices and vectors are recommended to be implemented by Matlab or Python.

受講および研究に関するアドバイス

Students are recommended to review the contents of the lecture after each class. Although the slides used in the lecture will be provided, taking notes is considered to be necessary, since the slides may not cover everything in the lecture. The algorithms learned during the class are recommended to be implemented by programming based on suitable code libraries or numerical programming environments.

教科書

書名 著者 出版社 ISBNコード 備考
Numerical Analysis 9th Ed. Richard L. Burden, J. Douglas Faires Brooks/Cole 978-0-538-73351-9

教科書(使用頻度、その他補足)

参考書

書名 著者 出版社 ISBNコード 備考
Numerical Recipes 3rd Ed. William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery Cambridge University Press 978-0-538-73351-9

参考書(使用頻度、その他補足)

参考になるwwwページ

授業内外における学生・教員間のコミュニケーションの方法

学生との直接対話

備考