Introduction to Numerical Analysis I, MATH 5610 (6860), Fall 2008, 8:35-9:25, LCB 225

Homework 1

Solutions

Due Monday, September, 8.

• 1.1: 18, 22, G26
• 1.2: 12, 22
• 1.3: 6, 8, 10, G14
• 2.1: 20
• 2.2: 8, 20, G24
• Email your code for algorithms 2.1, 2.2, The file should have the first three letters of your last name as a prefix, e.g. BLAbisect.m.

Homework 2

Solutions

Due Tuesday, September, 23.

• 2.3: 18 (also include 18(d). Newton's Method), 28
• Algorithms 2.3, 2.4, 2.5
• 2.4: 8, G14
• 2.5: 8, 14
• Algorithm 2.6
• Alogirthm 3.1
• 3.1: Part c of 6,8,10 (So you do 6c by hand, 8c with your code for Neville's Method, and 10c bound the error mathematically. Then compare the actual error to the theoretical bound you derive.)
• Alogirthm 3.2 (MatLab does not allow the index 0, so you need to shift all the indices in the psuedocode.)
• 3.2: 8 Clarification: You hand in #8 but not these suggestions - (not to be handed in: I would do 3 and 5 ...and 4 and 6.... for sure.)
• Algorithm 3.3 (again with the indices...)
• 3.3: 6

Homework 3

Solutions (This was corrected on October 13.)

Due Thursday, October, 9.

• 3.4: 4d, 8d
• 3.5: 2a, 2c
• 4.1: 6b, 8b, 29 (no looking up the answer), G28
• 4.2: 8
• 4.3: 2a, 6a, 16
• 4.4: 14, 22, Rarely Offered Bonus: 26
• Algorithm 4.1
• 4.6: 2f
• 4.7: 4f

Homework 4

Solutions

Due Friday, November, 7.

• Algorithm 6.1
• 6.1: 8d, 10
• Algorithm SP: This is my version combining Algorithms 6.2 and 6.3 with scaling at the beginning. After the scaling detailed in class, you can simply modify Algorithm 6.1 to perform a row swap that chooses the largest column element on or below the diagonal to use as the pivot element.
• 6.2: 18b (use Alg SP or ALG 6.3 if you wrote it)
• 6.3: 6
• 6.4: 12 a and b
• Algorithm 6.4
• 6.5: 2b, 6c
• Algorithm 6.5
• 6.6: 2, 4d

Homework 5

Solutions

Due Friday, November, 21.

• There are no problems to turn in for 7.1 and 7.2. You should still work a sufficient number of these exercises to be comfortable with the concepts from the sections.
• 7.3: 6c, 8c, 14c (14c was originally 10c, but I didn't mean that. If you did 10c, you can turn that it instead of 14c if you don't want to do 14c.)
• 7.4: 4d, 8
• 7.5: 4 (use Matlab's default precision (double)), 14
• You do not need to send me your algorithms.

Homework 6

Solutions

Due Monday, December, 8.

• 8.1: 8, G14 (yes this a G problem after a long absence)
• 8.2: 8d (you need the result of 7b applied to 1d, i.e f(x)=exp(x) on [0,2]), Bonus 14
• 8.3: 6
• 8.5: 4, 16
• 8.6: Since I won't cover this section until the due date, there is no formal homework. However, you should work multiple problems in this section.

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