Before you begin :
Do you really want to interpolate or just need to render an image from one file type to another? Making a larger image from a small file, will present you with challenges. It most certainly can be done. but the need is for a quality base image file is very important.
Interpolation (RIP) of a low-res, standard fair digital image will not render into a final print well at all. Yet, interpolation after an image such as a RAW image has been properly rendered into JEPG is quite possible to do.
Thus, the reason for defining your meaning of both ‘interpolation’ and ‘render’..
1) you probably don’t want to ‘interpret an image’ .. you need to ‘render the image’.
2) Are you beginning w/JPEG, TIF or RAW file?
3) The answer to #2 will drive the action in #1. Both will bring you to #4
4) Photoshop is the standard for this type of RIP (rasterized information protocol) activity .. in which you render a photo file (still in PPI (pixels per inch), before you output to DPI (dots per inch)
5) There are special RIP programs developed for specific Inkjet/large format printers that can render the image file into a printable file at large image sizes.
Got other questions .. fire away w/more detailed info. I can help if the info is provided.