Assignment 5 Solution

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Question 1: Let (1) = . Find the closed form of each of the following recurrence equations:

  1. ( ) = 2 (2) + log

  1. ( ) = 8 (2) + 2

  1. ( ) = 16 (2) + ( log )4

  1. ( ) = 7 (3) +

  1. ( ) = 9 (3) + 3 log

Question 2: Given two complex numbers, = + , = + , where a,b,c,d are real numbers.

Compute × by using only three real-number multiplications.

Question 3: Show the steps of Strassen’s algorithm to multiply the following two 4 X 4 matrices:

2

2

2

1

5

4

2

1

X=[5

8

3

2], Y=[7

1

4

4] .

3

3

5

9

4

8

6

3

1

3

4

2

5

7

4

2

To keep your answer shorter, you do not have to recursively apply Strassen’s algorithm to the subproblem on 2X2 matrices.

Question 4: Problem C-11.3 in the GT textbook

Put your answers in one file and submit to elearning.


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