MW 4-5:50, Randell 238B.

Instructor: Anatolii Grinshpan

Office hours: Tue, Thu 4-5 (Korman 247) or by appointment.

Course information. Math resource center. Academic Calendar.

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

Numerical Computing with MATLAB (C. Moler).

**Outline **

Sept 22. Introduction to the course.

Sept 24.

Operations count. A&H notes: 1.1, 1.2, 1.3. Homework 1, due October 1. Week 1 exercises.

Sept 29. Nested multiplication and long division. Approximation of irrational numbers.

Oct 1. Quiz 1 (

Week 1 answers. Homework 2, due October 8. Week 2 exercises.

Oct 6. Babylonian numerals. Octal and hexadecimal systems. Error, absolute and relative error. Significant digits.

A&H notes: 2.2

Oct 8. Quiz 2 (binary/denary arithmetic, polynomial evaluation). Error classification.

Modes of rounding. Loss of significance
error. Propagation of error in function evaluation.

A&H
notes: 2.3.
Week 2 answers. Homework 3, due October 15. Week 3 exercises.

Oct 13. No class: Columbus day.

Oct 15. Propagation of error in arithmetic operations. Noise in evaluation. Underflow/overflow.

Fixed-point and floating-point representations of numbers.

A&H notes: 2.1. Week 3 answers. Homework 4, due October 22. Week 4 exercises.

Oct 20. Subnormal numbers and biased exponents. Single (32-bit), double (64-bit), and extended (80-bit) precision models.

“1-byte” floating-point model. Rounding estimates. A&H notes: 2.4 (summation example).

Example: summing in 1-byte format. Additional material: Goldberg’s paper on IEEE.

Oct 22. Quiz 3 (error arithmetic, floating-point format). Discussion. Practice test. Week 4 answers. Homework 5: none.

Oct 27. Midterm 1 (lectures of Sept 22 – Oct 22, homework, exercises, quizzes). Answers. Extra credit: Kahan’s algorithm.

Oct 29. Iterations
and rootfinding. Rate and
order of convergence. Bisection and

A&H notes: 3.1, 3.2. Homework 6, due November 5. Week 6 exercises.

Additional reading: introduction to MATLAB (1.1, 1.2), zeros and roots.

Nov 3. Midterm
1 discussion. Examples on

Nov 5. Division via

Handout: a chaotic search for i (hardcopy). A&H notes: 3.3. Week 6 answers.

Nov 10. Quiz 4 (rootfinding). Fixed point iterations.

A&H notes: 3.4. Homework 7, due November 17 .

Nov 12. Behavior of fixed point iterates. Types of fixed points. Contractive mapping theorem: proof.

Examples. Week 7 exercises.

Nov 17. Quiz 5 (fixed point iterations). Aitken’s extrapolation formula. Logistic map. An example.

Week 7 answers. Week 8 exercises. Homework 8: none.

Nov 19. Logistic map (continued). Stability of roots. Wilkinson’s example.

Something to play with. A&H notes: 3.5 . Practice test. Answers.

Nov 24. Midterm 2 (lectures of Oct 29 – Nov 19, homework, exercises, quizzes). Answers. Problem 3B. Problem 4B.

Dec 1. Lagrange and

Dec 3. The minimax problem. Chebyshev polynomials.

Animations for Chebyshev polynomials.

A&H notes: 4.2, 4.4, 4.5. Exercises on interpolation.

Dec 5. Office hours 2-3 P.M., Korman 255.

Dec 9. Office hours: 12-2 P.M., Korman 247. Practice exam. Answers.

Dec 10. Office hours: 1:30-2:15 P.M. Korman 255. Answers to exercises. Graphs.

Dec 11. Office hours: 1-2 P.M., Korman 255.

Dec 12. Final exam (all lectures, homework, quizzes, exercises): 8-10 A.M., Randell 231.

Answers. Problem 6.