Math. 555-01, Fall, 1997 Assignments
/ Assignments / Exams
This list is updated as the assignments are made and exam dates
1. For Friday, September 5:
2. For Wednesday, September 10:
- Read Section 1.1.
- Do problems 1.2 and 1.3 on page 53 of the text.
For Friday, September 12 :
- Read and review all of Chapter 1 through Section 1.5
- Do problems 1.5 and 1.8 on pp. 54-55 of the text.
3. For Monday, September 15:
- Read through Section 2.1 of the text.
- Read the handout, and read 2.2.1, pp. 78-82 of Rigorous Global Search:
Continuous Problems (available on reserve in Dupre Library or on the
Ultra system at /home/rbk5287/reports/opt-book/book.dvi or /home/rbk5287/reports/opt-book/book.ps.
(Please only reproduce the relevant sections, to respect Kluwer's copyright.)
4. For Wednesday, September 17:
- Do problems 1.14, 1.16, and 1.17 on pp. 57-58 of the text.
- Study Section 2.1, and, in particular, the material on pp. 80-88 dealing
with pivoting, factorizations of symmetric matrices, and iterative refinement.
5. For Monday, September 22:
- Hand in problems 2.1 and 2.2 on p. 121 of the text.
- Study section 2.2 (norms and condition numbers)
6. For Friday, September 26:
- Hand in problem 2.3, p. 121 and 2.9, p. 122 of the text.
For Wednesday, October 8 (tentative):
- Study sections 2.2, 2.3 and 2.4 of the text.
- Hand in exercises 2.17
7. For Monday, October 13:
- Study all of Section 3.1 carefully.
8. For Monday, October 20:
- Hand in problems 2.22 and 2.23 from page 126.
9. For Monday, October 27:
- Study Sections 3.2, 3.3, and 3.4 carefully.
- Hand in problems 3.1, 3.3, and 3.5 (use a divided difference table
as indicated in class) from pp. 197--198
- Do problem 3.11 (you may use Netscape instead of FTP; start at
10. For Friday, October 31:
- Study Sections 4.1, 4.2, and 4.3 of the text.
- Hand in problems 4.1, 4.5, 4.7, and 4.12 on pp. 262-265.
11. For Monday, November 10:
- Problem 2.21, p. 125 of text.
12. For Monday, November 24:
- Hand in problem 4.15, p. 265 of text.
- Study sections 5.1 and 5.2 of the text.
- Study as much of section 5.3 as possible.
13. For early next semester:
- Make sure sections 5.1, 5.2, quasi-Newton methods and continuation
methods from 5.3, 5.4, and 5.5 are thoroughly studied.
- Hand in problems 5.1 (you may use either MATLAB or Fortran), 5.2, 5.4.
- Hand in 5.10.
The final exam will be in-class, open-book, on
Friday, December 12 at 10:15-12:45, in the Conference Room (MDD 206). Pay
careful attention to the following:
- The forward and backward modes of automatic differentiation,
for both one and more than one variable.
- Upward rounding, downward rounding, round-to-nearest,
and (for interval arithmetic) outward rounding.
- Numerical stability of expressions (e.g. avoiding
subtraction of almost equal numbers).
- The condition number of a computation.
- Elementary interval arithmetic.
- The mean value form for an interval enclosure
for a function.
- Why partial pivoting is required in Gaussian
- Definition and elementary properties of vector
- Definition and elementary properties of derived
- Equivalence of norms in n-space.
- The condition number of a matrix.
- The form of the Lagrange interpolating polynomial.
- The form of the Newton interpolating polynomial.
- The error formula for an interpolating polynomial,
both as a divided difference and in terms of a derivative.
- Hermite interpolation and more general interpolation
as limiting cases of Newton interpolation.
- Computing Hermite interpolants with a divided
- Failure of interpolation with equi-spaced points
for Runge's function.
- The midpoint bisection algorithm and its convergence.
- Line searches. (Be prepared to do a simple one-dimensional
line search as described on pp. 257-259. You may want to look up golden
section search in other texts, too.)
- The multivariate Newton method and its convergence
(or lack thereof).
- The Krawczyk operator for nonlinear systems of
- Descent methods with line searches:
- Steepest descent
- Descent using the Newton direction as search
- The conjugate gradient method.