**Tom Kelliher, CS 315**

**Apr. 14, 1999**

Read 3.3.

Linear array multiplication example, run time calculation.

- Returning to the run time.
- Three optimizations.
- Convolution, connections.

Shuffle-exchange networks.

- Run time, efficiency, work.
What did we forget about in the run time calculation?

- Merging adjacent cells.
- Reworked example.
- Changes to run time, efficiency, work?

- All input from one side of array.
- Reworked example.
- Changes to run time, efficiency, work?

Using the original array to perform two multiplications in parallel.

Show that this algorithm is optimal for a linear array.

The convolution of the **N**-vectors and
is the **2N - 1** vector where

where .

- How does this relate to integer multiplication?
- How does this relate to polynomial multiplication?
- Use in signal processing.

Wed Apr 14 10:10:05 EDT 1999