# Math 300 – Numerical Analysis, Spring 2009.

WF 12-1:50, Curtis 452.

Instructor: Anatolii Grinshpan
Office hours:  M 2-3, W 3-5 (Korman 247) or by appointment.

Elementary Numerical Analysis (K. Atkinson and W. Han).

Numerical Computing with MATLAB (C. Moler).

Outline

Apr 1. Introduction to the course. Number systems: decimal and binary arithmetic.

A & H notes: Modeling, Appendix E.

Apr 3. More on binary arithmetic. Octal, hexadecimal, Mayan, and Babylonian systems.

A & H notes: 2.2

Apr 8. Quiz 1 (denary and binary arithmetic). More on errors. Approximation of irrational numbers.

Apr 10. Propagation of error in function evaluation and arithmetic operations.

A & H notes: 2.3.

Apr 15. Four modes of rounding. Polynomial evaluation and operation count. Nested multiplication.

A & H notes: 1.3. Week 1 answers. Homework 2, due April 22.

Apr 17. Quiz 2 (error arithmetic and propagation). Fixed-point and floating-point representations of numbers.

A & H notes: 2.1.

Apr 22. Subnormal numbers and biased exponents. IEEE single-precision format. “1-byte” floating-point model

Week 2 answers. Homework 3, due April 29. Notes on IEEE: Overton, Goldberg.

Apr 24. Quiz 3 (IEEE format). Correctly rounded operations. Rounding estimates. Summation.

A & H notes: 2.4 (summation example). Summing in 1-byte format.

Apr 29. Week 3 answers. Midterm 1 (lectures of April 1 – April 24).

Extra credit: Kahan’s algorithm, plot the absolute relative error of the IEEE floating-point representation (single or double precision).

May 1.  Exam discussion. Taylor polynomials.

A & H notes: 1.1

May 6.  Taylor polynomials. Error sequences: order and rate.

May 8. Quiz 4 (Taylor polynomials). Rootfinding. Bisection.

A & H notes: 3.1.

May 13. Week 6 answers. Newton’s method.

A & H notes: 3.2. Homework 5, due May 20.

May 15. Division via Newton’s iteration. Stability of roots.

A & H notes: 3.5.

May 20. Quiz 5 (Bisection and Newton’s method). Secant method.

Week 7 answers. A & H notes: 3.3.

May 22. The order and rate of the secant method. Homework discussion.

May 27. Midterm2 (lectures of May 1 – May 22).

May 29. Fixed-point iteration. The contraction mapping theorem.

A & H notes: 3.4. Homework 6, due June 5 .

June 3.  Quiz 6 (fixed points). Fixed-point iteration: example, animation.

Lagrange interpolation.

A & H notes: 4.1, example.

June 5. Newton interpolation and interpolation error. The minimax problem.

Week 9 & 10 answers, graphs. A & H notes: 4.2, 4.4, 4.5.

Office hours: June 8, 2-3 (Korman 247), 3-4+ (Korman 253).

June 10. Final Exam (all lectures), 1-3 P.M., Curtis 451. Answers.