University of Arizona | Department of Mathematics | Misha Stepanov | MATH 575A

MATH 575A
Numerical Analysis

Section 001, Fall 2009

Classroom: MATH 501, TR, 11:00am–12:15pm
Instructor: Misha Stepanov
office: MATH 623
e-mail: stepanov@math.arizona.edu
phone: (520) 621-2685
Office Hours:  Tue 10–11am, Wed 2–3pm (in MATHE 145), Thu 9–10am (subject to change) and by appointment
Super TA:  Matt Pennybacker
Text:  numerical linear algebra book L.N. Trefethen, D. Bau III,
Numerical Linear Algebra
(SIAM, 1997)

Important note
• 128 × 128 matrix from EIG homework is changed.
• Solution of Midterm (PDF) is posted.

Homework: Homework will be assigned regularly. Selected homework will be graded, and a final score of 250 points will be assigned. Homework is an essential component of the course, whether it is assigned for grading or not. Homework could be turned in in 1) class; 2) MATH 108 room (before 4:30pm); 3) MATH 623 office (slide it under the door if I'm not there); 4) e-mail message; 5) a website (send me a link to it then). If the homework problem assumes writing a code and running it, you can use any language you like (MATLAB, C, Fortran, …), even if the text mentions MATLAB.

EIG • Find the eigenvalues of the 4 × 4 matrix.
• Find the maximal and the minimal (in absolute value) eigenvalues of the 128 × 128 matrix.
• Find at least one eigenvalue (with corresponding eigenvector) of the 10000 × 10000 matrix A = B + 10-5 u u*. The vector u = (1, 1, 1, …, 1)*. The sparse matrix B is described by the following data. The data format is the following: Each data row corresponds to a row of the matrix. The positions of non-zero matrix elements (all of which are equal to 1) are listed (the data entry “0” means that there are no more).		 Due Dec 8
HW11 Lecture 29: 29.1. Due Dec 1
HW10 Lecture 24: 24.1, 24.3.
Lecture 25: 25.1, 25.2.
Lecture 27: 27.3, 27.5, 27.6.		 Due Nov 24
HW9 Lecture 20: 20.1, 20.2.
Lecture 21: 21.2, 21.6.
Lecture 22: 22.2.		 Due Nov 10
HW8 Lecture 11: 11.1, 11.2, 11.3.
Lecture 18: 18.1, 18.2.
Lecture 19: 19.1, 19.2.		 Due Nov 3
HW7 Lecture 16: 16.1.
Lecture 17: 17.2. Also implement algorithm 17.1 and test it on random triangular matrices.
QR, quality.		 Due Oct 20
HW6 Lecture 8: 8.2 (implement also classical Gram-Schmidt (algorithm 7.1)), 8.3.
Lecture 9: 9.1, 9.2. Also reproduce experiment 2 (here is an example of matrix A for not MATLAB users).
9.1, Legendre polynomials		 Due Oct 13
HW5 Lecture 6: 6.2, 6.3, 6.4.
Lecture 10: 10.1, 10.2, 10.4.
QR, numerical example.		 Due Oct 1
HW4 Lecture 4: 4.1, 4.2, 4.4, 4.5.
Lecture 5: 5.2, 5.3, 5.4.		 Due Sep 24
HW3 Lecture 2: 2.1, 2.3, 2.4, 2.6.
Lecture 3: 3.2, 3.3, 3.4, 3.5.
Lecture 12: 12.1.		 Due Sep 17
HW2 Lecture 15: 15.1(abcdef).
Lecture 1: 1.1, 1.3, 1.4.
Stability, series. 		Due Sep 10
HW1 Lecture 13: 13.1, 13.2, 13.3.
Lecture 14: 14.1, 14.2.
Calculate ζ(4) = 1 + 1 / 24 + 1 / 34 + 1 / 44 + ... as a sum of inverse 4th powers of integers as accurately as you can (15 significant digits is enough).
Floating point.		 Due Sep 3

Grades: The total number of points available on homework and tests is 500 = 250(homeworks) + 100(test) + 150(final exam). The one in-class test is scheduled for Tue, Oct 27. The final exam is at Thu, Dec 17, 11:00am–1:00pm, in the same room where the class met all semester. The University's Exam regulations for final exam week will be strictly followed, in particular those regarding students with multiple exams on a single day. The regulations can be found at registrar.arizona.edu/schedule094/exams/examrules.htm.