Similar to some of the topics touched on in this question, Is it important to reboot Linux after a kernel update?, I was curious if there was a way in which one could apply kernel updates to the system without rebooting. I know that there is a vendor called Ksplice that offer features like this. However, I was curious if there was a way to perform this same task without a commercial offering or perhaps an alternative to Ksplice since it looks like some of the feature sets may have changed since they were purchased by Oracle. Ideally, if there is a script or way that I can add some files to perform this on CentOS, Red Hat, and/or Ubuntu would be great.
KSplice was a novel piece of code and nothing similar has been written for Linux. While it possible (and probable) that somebody can fork the old open source code and continue development, there are presently no alternative pieces of software in distribution for hot patching a running Linux kernel.
kexec is a nice way of doing fast reboot. While this isn't 'live upgrading your kernel', it does some interesting things such as bypassing BIOS, POST and BootLoader...
Some additional informations can be found through Ubuntu 'RapidReboot' topic : https://wiki.ubuntu.com/RapidReboot
(Disclosure: I work for Canonical)
Since you asked, for Ubuntu specifically, Canonical now delivers this service on 16.04.
This uses the live patching technology in the upstream Linux kernel since 4.0 was released.