|
|||
CAAM 454NUMERICAL ANALYSIS II Spring 2009 |
|||
|
Lectures
Week 15 (April 14+16, 2009)
Introduction to Linear Programming
Reading: Sections 13.1-13-3 and 14.1, 14.2 in
J. Nocedal and S. J. Wright: Numerical Optimization.
Week 14 (April 7+9, 2009)
Solution of systems of nonlinear equations
Reading: Chapter 11 in
J. Nocedal and S. J. Wright: Numerical Optimization.
Handout: Chapter 9.
Week 13 (March 31, 2009 (Thursday April 2 is spring recess))
Nonlinear Least Squares
Reading: Chapter 10 in
J. Nocedal and S. J. Wright: Numerical Optimization.
Handout: Chapter 7.
Week 12 (March 24+26, 2009)
Solution of the trust-region subproblem; introduction to quasi-Newton methods
Reading: Chapters 4 and 6 in
J. Nocedal and S. J. Wright: Numerical Optimization.
Handout: Chapters 5 and 6.
Week 11 (March 17+19, 2009)
Line search methods and trust-region methods
Reading: Chapters 3 and 4 in
J. Nocedal and S. J. Wright: Numerical Optimization.
Handout: Chapter 5.
Matlab: line_search.zip.
Week 10 (March 10+12, 2009)
Local convergence of Newton and Newton-type methods, line search methods.
Reading: Chapter 3 in
J. Nocedal and S. J. Wright: Numerical Optimization.
Handout: Chapter 4 and 5.
Week 9
Spring BreakWeek 8 (Feb 24+26, 2009)
Overview of methods for unconstrained optimization, convergence of sequences, local convergence of Newton and Newton-type methods.
Reading: Section 2.2, 3.3, 7.1 in
J. Nocedal and S. J. Wright: Numerical Optimization.
Handout: Chapter 3 and 4.
Week 7 (Feb 17+19, 2009)
Note: This week we will have an extra lecture on Thursday 2/19, 4pm-5:30pm in KH 105Convergence analysis of Krylov subspace methods, preconditioning. Introduction to unconstrained optimization
Reading: Lectures 38, 35, 40 in
Lloyd N. Trefethen and David Bau, III: Numerical Linear Algebra.
Reading: Chapter 1 and Section 2.1 in
J. Nocedal and S. J. Wright: Numerical Optimization.
Additional Reading: Sections 6.11, 9.2, 9.3 in
Y. Saad: Iterative methods for sparse linear systems
Handout: Chapter 2 and 3.
Week 6 (Feb 10+12, 2009)
Note: This week we will have an extra lecture on Thursday 2/12, 4pm-5:30pm in KH 105The conjugate gradient method; convergence analysis of Krylov subspace methods
Reading: Lectures 38 and 35 in
Lloyd N. Trefethen and David Bau, III: Numerical Linear Algebra.
Additional Reading: Sections 6.7, 6.11 in
Y. Saad: Iterative methods for sparse linear systems
Handout: Chapter 2.
Week 5 (Feb 3+5, 2009)
The Arnoldi iteration; GMRES; Lanczos
Reading: Lectures 33, 35, 36 in
Lloyd N. Trefethen and David Bau, III: Numerical Linear Algebra.
Additional Reading: Sections 6.1, 6.2, 6.3, 6.5.1-6.5.4, 6.6 in
Y. Saad: Iterative methods for sparse linear systems
Handout: Chapter 2.
Matlab: GMRES implementations mygmres.m,
mygmres_simple.m,
gmres_driver.m,
giv_rot.m (used in mygmres.m).
Week 4 (Jan. 27 + 29, 2009)
No class. Classes will be made up in February.Week 3 (Jan. 20 + 22, 2009)
Introduction to Krylov subspace methods; background.
Reading: Lectures 32 in
Lloyd N. Trefethen and David Bau, III: Numerical Linear Algebra.
Additional Reading: Sections 5.1, 5.2, 6.1, 6.2 in
Y. Saad: Iterative methods for sparse linear systems
Handout: Chapter 2.
Week 2 (Jan. 13 + 15, 2009)
Convergence results for Jacobi, Gauss-Seidel, SOR; Application to linear system arising from finite difference discretizations of differential equations.
Reading: Section 4.2.3 - 4.2.5 in
Y. Saad: Iterative methods for sparse linear systems
For background material on finite difference approximations read
Section 2.1 and 2.2 in
Y. Saad: Iterative methods for sparse linear systems
Handout: Chapter 1.
Matlab: adv_diff_bvp.m,
adv_diff_bvp_radii.m.
Week 1 (Jan. 6 + 8, 2009)
Basic iterative methods; Jacobi, Gauss-Seidel, SOR; Convergence of basic iterative methods.
Reading: Section 4.1.1 - 4.2.1 in
Y. Saad: Iterative methods for sparse linear systems
Handout: Chapter 1.
This web page is maintained by Matthias Heinkenschloss.