Fall 2024 University of Nevada Reno

**Math 466/666 NUMERICAL METHODS I (3+0) 3 credits**

Numerical solution of linear systems, including linear programming; iterative solutions of non-linear equations; computation of eigenvalues and eigenvectors, matrix diagonalization. Prerequisite(s): MATH 330.

Instructor Course Section Time Room ------------------------------------------------------------------------ Eric Olson Math 466/666 Numerical Methods I MWF noon-12:50pm DMSC106

- Instructor:
- Eric Olson
- email:
- Please contact me through WebCampus
- Office:
- MWF 11:00-11:50PM in DMS 238 and through Zoom by appointment
- Homepage:
- http://fractal.math.unr.edu/~ejolson/466/
- Grader:
- to be determined (contact through
WebCampus)
- Course Textbook:
- Endre Suli, David F. Mayers,
*An Introduction to Numerical Analysis*, 1st Edition, Cambridge University Press, 2003. - Supplemental References:
- Hosking,
Joe, Joyce and Turner,
*First Steps in Numerical Analysis*, 2nd Edition, Arnold, 1996. - Jeffery Leader,
*Numerical Analysis and Scientific Computation,*Pearson, 2004. - Lloyd Trefethen,
*Numerical Linear Algebra*, Siam 1997. - Justin Solomon,
*Numerical Algorithms: Methods for Computer Vision, Machine Learning and Graphics*, CRC Press, 2015. - Anthony Ralston and Philip Rabinowitz, A First Course in Numerical
Analysis, Second Edition, Dover, 1978.
- Richard Hamming,
*Numerical Methods for Scientists and Engineers, Second Edition*, Dover, 1986.

*The Julia 1.6 Language*, official documentation and software download.- Thomas Breloff,
*Plots--Powerful Convenience for Visualization in Julia*.

- The effects of rouding error in numerical computation.
- Newton's method, interpolation and numerical Linear Algebra.
- Practical use of the computer to solve numerical problems.

- HW1 problems 1.1, 1.4 and 1.6 due Sept 23 (solutions).
- HW2 problems 2.1, 2.8i,ii due Nov 8
- HW3 problems 2.9, 2.10 and 2.12 due Nov 22

- Lecture 1: Newton's Method
- Lecture 2: Taylor's Theorem
- Lecture 3: Fixed-point Methods
- Lecture 4: Newton with Julia
- Lab 1/Lecture 5: Getting Started Cut and Paste
- Lecture 6: Relaxation Method
- Lecture 7: The Secant Method
- Lecture 8: Bisection Method
- Lecture 9: Review of Newton
- Lecture 10: Secant with Julia (newton.jl, relaxation.jl, secant.jl)
- Lab 2/Lecture 11: Newton's Method Verfication of Order
- Lecture 12: Determinants
- Lecture 13: Pivoting Example
- Lecture 14: LU Factorization with Julia
- Lecture 15: Vector Norms
- Lecture 16: Cauchy and Hölder Inequalities
- Lecture 17: Matrix Norms
- Lecture 18: More Matrix Norms
- Lecture 19: The Condition Number
- Lecture 20: Relative Error in Double Precision
- Lecture 21: Conditioning Examples
- Lecture 22: The Power Method
- Lecture 23: Inverse Power Method
- Lab 3: FLOPS and Time Complexity
- Lecture 24: Nonlinear Systems
- Lecture 25: Contraction Mapping Theorem
- Lab 4: Spectral Norm Additional Notes
- Lecture 26:
||Dg(ξ)||
_{∞}< 1 Implies Contraction

- Nicholas Higham, Estimating the matrix p-norm,
*Numer. Math.*, vol 62, 1992, pp. 539-555.

- Review HW1 questions and answers.
- Know the proof of Taylor's theorem.
- Be able to state Newton's method, the secant method and the bisection method.
- Show that Newton's method is quadratically convergent.

We will be using WebCampus to turn in written homework--either scanned from pencil and paper or prepared digitally using an iPad or similar device. There will also be a number of in-class computing labs. In addition to the computing labs and written homework, there will be two exams and a final exam. In person attendance is mandatory for all exams and the final.

Theoretical Midterm 50 points Practical Midterm 50 points Homework 50 points Computer Labs 50 points Final 100 points ------------------------------------------ 300 points totalExams and quizzes will be interpreted according to the following grading scale:

Grade Minimum Percentage A 90 % B 80 % C 70 % D 60 %The instructor reserves the right to give plus or minus grades and higher grades than shown on the scale if it is believed they are warranted.

Aug 26 -- Newton's Method Aug 28 -- Taylor's Theorem Aug 30 -- Fixed-point Methods Sep 02 ***Labor Day*** Sep 04 -- Newton with Julia Sep 06 -- Lab 1 Quadratic Equations Sep 09 -- More Fixed-point Methods Sep 11 -- The Secant Method Sep 13 -- The Bisection Method Sep 16 -- Review of Newton's Method Sep 18 -- Secant with with Julia Sep 20 -- Lab 2 Newton's Method Sep 23 -- Solution by Elimination Sep 25 -- Gaussian Elimination and Pivoting Sep 27 -- LU Factorization with Julia Sep 30 -- Vector and Matrix Norms Oct 02 -- Theoretical Midterm Oct 04 -- Ill-conditioning Oct 07 -- Minkowsky Inequality Oct 09 -- The Matrix p Norm Oct 11 -- The Condition Number Oct 14 -- Double Precision Arithmetic Oct 16 -- Interpretation of Condition Number Oct 18 -- Power Method for the Matrix 2 Norm Oct 21 -- Finding the Norm of Inv(A) Oct 23 -- Lab 3 FLOPS when Solving Ax=b Oct 25 ***Nevada Day*** Oct 28 -- Solution of Nonlinear Systems Oct 30 -- The Contraction Mapping Theorem Nov 01 -- Lab 4 The Spectral Norm Nov 04 -- Derivative Condition for Contraction Nov 06 -- Nov 08 -- Lab 5 Nov 11 ***Veteran's Day*** Nov 13 -- Nov 15 -- Lab 6 Nov 18 -- Nov 20 -- Nov 22 -- Lab 7 Nov 25 -- Nov 27 -- Nov 29 ***Family Day*** Dec 02 -- Computer Exam Dec 04 -- Dec 06 -- Dec 09 -- In-class Review Dec 11 ***Prep Day*** Dec ?? Final Exam from ??:??-?:??pm

Exams and quizzes, unless otherwise noted, will be closed book, closed notes and must reflect your own independent work.

If you are unclear as to what constitutes cheating, please consult with me.

Last Updated: Mon Aug 26 11:42:57 AM PDT 2024