# ## 주메뉴

### 수치해석 (2011년 1학기)

• 연세대학교
• 정윤모 • 주제분류
자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
• 등록일자
2011.03.14
• 조회수
9,366
•
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.
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 #### 연관 자료 #### 사용자 의견

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