Numerical Algorithms

There will be N ≅ 6 homework assigments, a final project, and an exam and re-take. The homework assignments will be published on Canvas after the exercise class on Tuesday, and have to be handed in the next Monday. The homework assigments can be made in groups of two, the final project has to be made in groups of three (or two when this is unavoidable).

When all grades, except for at most one homework assignment, are not less than 4, then with H denoting the average of the best N-2 grades for the homework assignments, P the grade for the final project, and T the grade for the exam or re-take, the final grade E, averaged in the usual way, is given by E=max(T,(4H+3P+3T)/10). In all other cases, E=T.

Grades obtained in previous years for homework assignments or for the project are no longer valid.

Book: Michael T. Heath, Scientific Computing, An Introductory Survey, Second Edition (see Canvas).

Material Covered

• week 44 Monday: Ch. 1. until §1.3.8.
• week 44 Friday: Rest of Ch. 1, Ch.2 until §2.3.3.
• week 45 Monday: Ch. 2 until §2.4.7.
• week 45 Friday: Rest Ch. 2 without §2.4.8, 2.4.10, 2.5.2. Ch. 3 until §3.3.
• week 46 Monday: Continue with Ch. 3.
• week 46 Friday: Ch. 3 until §3.5.3.
• week 47 Monday: Rest Ch. 3 without QR with column pivoting, and total least squares. Ch. 4 until §4.2.3.
• week 47 Friday: Rest Ch. 4 without QR iteration with shifts, §4.5.7-12, 4.7-9. §5.1.1.
• week 48 Monday: Rest Ch. 5 without §5.3, 5.5.5-8, 5.6.4.
• week 48 Friday: Ch. 6, without pp. 267-268, §6.3, 6.4.4, 6.5.4-7, 6.6, pp. 289-298.
• week 49 Monday: §7.1, 7.2, 7.3.
• week 49 Friday: Rest Ch. 7 without p. 320, pp. 322-223. Ch. 8 until §8.3.1
• week 50 Monday: Rest Ch. 8 without §8.3.2, 8.3.4, 8.4-9. Ch. 9 until p388.
• week 50 Friday: Rest Ch. 9 until p404.

Exercises

• week 44 Mon/Tue: Ch. 1. Exer. 2, 4, 5, 10, 12. Comp. exer. 4, 7.
• week 44 Friday: Attached exercises, Ch. 2: 2, 3, 4, 8, 10, 12.
• week 45 Mon/Tue: Ch. 2: 7, 16, 18, 23, 25, 27, 37(a). Comp. exer. 2, 6 (up to the part about condition estimators)
• week 45 Friday: Ch. 3: 1, 2, 4, 5, 11, 13, 14. Comp exer: 1, 3a The following functions/modules may be useful: numpy.polyfit (fitting polynomials), scipy.linalg.solve (solving linear systems), numpy.poly1d (representing and evaluating polynomials), time (timing)
• week 46 Mon/Tue: Ch. 3: 16, 17, 18abc, 22, 25. Computer exercises: 5ab, 10
• week 46 Friday: Ch 4: 3 (a)-(d), 6, 7, 8, 9, 10, 15, 16, 19, 2
• week 47 Mon/Tue: Ch. 4: 20a),b), 23. Computer exercises: 2, 3, 4
• week 47 Friday: no new exercises.
• week 48 Mon/Tue: Ch. 5: 1, 6, 10, 11, 12. Computer exercise 3, 18.
• week 48 Friday: Ch. 6: 1(b,d), 2(b,c), 3(b,d), 4(b,d), 5(b,c), 6(a,c), 7 (only first order conditions). Computer exercise: 2, 7.
• week 49 Mon/Tue: Ch. 7: 1, 5, 6, 10. Comp. exer. 7.1, 7.5a)
• week 49 Friday: Ch. 7: 15. Comp. exer. 2 (a,b). Ch. 8: 1, 3, 5. Comp. exer. 6
• week 50 Mon/Tue: Ch. 7: 12. Comp exer. 6. Ch. 8: 6, 12
• week 50 Friday: Ch. 9: 1, 3, 4, 7. Comp. exer. 1