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.

Course information.   Math resource center.   Academic Calendar.

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.

           Error, absolute and relative error. Significant digits.

           A & H notes: 2.2

 

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

           Homework 1, due April 15. 

 

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.

             Homework 4, due May 13.

 

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.