I use Lancos algorithm or resize in PS. Both of which seem to do a good job for amateur use. I done some trials for myself little while ago resizing up, and down PSP wasn't so good. Most studio's and professionals use 'Best Color' which don't come cheap !

And every one said, 'If we only live,
We too will go to sea in a Sieve,---
To the hills of the Chankly Bore!'
Far and few, far and few, Are the lands where the Jumblies live;
Their heads are green, and their hands are blue, And they went to sea in a Sieve.

Edward Lear
http://www.nonsenselit.org/Lear/ns/jumblies.html