Is Tiger 10.4.11 upgrade to Leopard possible?

Is it possible or even desirable to install Leopard 10.5. on a iMac G4 15" display with 800mhz processor and 1 gig of ram. I don't want to lose the ability to access my Tiger programs or files but I have a lot of software for 10.5 that I can't currently run. Thanks.

looks like your processor may be too slow - below states 867MHz or faster needed

Mac OS X 10.5 - Technical Specifications

That machine would be likely to be eight to ten years old now. I'm afraid that the ugly truth is that you're going to need to modernize both your computer and software programs. You don't have to get something BRAND new, but I'd suggest something fairly recent. That G4 is now VERY VERY unsafe on the Internet anyway due to un-upgradable software.

Thanks for the quick and concise answers. I will be looking to upgrade to a more modern and powerful machine in the near future.

If your budget will cover it, here is the minimum spec equipment I would be looking for right now
OS X Mavericks: System Requirements

This will allow you to run the latest OS version, OS X 10.9 (Mavericks)

I'd suggest something from 2010 or newer if affordable. Apple's refurbs are a great value as well, and come with a warranty.