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This list is updated as the assignments are made and exam dates
are set.

- Read Section 1.1.
- Do problems 1.2 and 1.3 on page 53 of the text.

- 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.

- 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.)

- 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.

- Hand in problems 2.1 and 2.2 on p. 121 of the text.
- Study section 2.2 (norms and condition numbers)

- Hand in problem 2.3, p. 121 and 2.9, p. 122 of the text.

- Study sections 2.2, 2.3 and 2.4 of the text.
- Hand in exercises 2.17

- Study all of Section 3.1 carefully.

- Hand in problems 2.22 and 2.23 from page 126.

- 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
`http://www.netlib.org/`)

- 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.

- Problem 2.21, p. 125 of text.

- 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.

- 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 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 elimination.
- Definition and elementary properties of vector norms.
- Definition and elementary properties of derived matrix norms.
- 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 difference table.
- 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 equations.
- Descent methods with line searches:
- Steepest descent
- Descent using the Newton direction as search (pp. 304-306).
- The conjugate gradient method.