수치해석 (2011년 1학기)

연세대학교
정윤모

페이스북 트위터 카카오톡 네이버밴드 링크복사

주제분류

자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
등록일자

2011.03.14

조회수

10,080

This course is designed to acquaint students in mathematical and physical sciences and engineering with the fundamental theory of numerical analysis. This course is devoted to nonlinear equations, optimization, approximation theory, numerical quadrature and numerical linear algebra (including linear systems, least squares problems and eigenvalue problems). The course will stress both on analytic and computational aspects of numerical methods.

수강안내 및 수강신청
※ 수강확인증 발급을 위해서는 수강신청이 필요합니다

System of linear equation 1-1

차시별 강의

1.	System of linear equation 1-1	linear equation
	System of linear equation 1-2	linear equation
2.	System of linear equation 2	linear equation, condition number
3.	System of linear equation 3-1	Posteriori analysis, Lu factorization
	System of linear equation 3-2	Lu factorization, Pivoting
4.	Special types of matrices	Cholesky factorization
5.	Linear least square1	least square, normal equation
	Linear least square2	least square, QR decomposition
6.	Linear least square3 (SVD)	Singular Value Decomposition (SVD)
7.	Linear least square4 (SVD)	Pseudo-Inverse, Rank deficient least square
	Linear least square5	Householder transformation, Given rotation
8.	Iterative methods	iterative method
9.	Iterative methods2	Jacobi method, Gauss-Seidal method
	Iterative methods3	SOR(Successive overrelaxation), Gradient method
10.	Iterative methods4	Gradient method
11.	Iterative method5	Conjugate gradient method
	Iterative method6	Generalize of Conjugate gradient mehtod
12.	Eigenvalue problem1	eigenvalue decomposition, algebraic multiplication, geometric multiplication
	Eigenvalue problem2	Schur canonical form, Schurs unitary triangularization, Gershgorin
13.	Eigenvalue problem3	Power iteration, Inverse iteration
14.	Eigenvalue problem4	Orthogonal iteration, QR iteration
	Eigenvalue problem5	Upper Hessenberg form
15.	Eigenvalue problem6	Rayleigh-Ritz quotient
16.	Nonlinear equations1	Sensitivity & conditioning, Bisection method
	Nonlinear equations2	Newton method, secant method, contrative mapping thm
17.	Nonlinear equations3	Quadratic convergence of newton method, Broydens method
18.	Nonlinear equations4	Fixed pt method
	Optimization1	Existence & Uniqueness, Optimization in 1-D
19.	Optimization2	line search method, trast region method, armijo condition, curvature condition, back tracking method
20.	Optimization3	Quasi-Newton method, Secant-like method, BFGS method
	Optimization4	Nonlinear least square, newton method, gauss-newton method, constrained optimization, feasible direction, lagrangian function
21.	Optimization5 , Interpolation1	Penalty method, Barrier method, polynomial interpolation, monimial basis, horners method
22.	Interpolation2	Lagrange interpolation, Newton interpolation
	Interpolation3	Runges counter example, Cubic spline interpolation
23.	Interpolation4, Numerical integration1