Change to a higher resolution on a pic

[rich2005]

The question is about up-scaling an image rather than improving the quality of a small image.

By all means use an on-line conversion but that does not give you much insight as to Gimp functions.

The Gimp Scale with No-Halo interpolation has a measure of built in smoothing and might be sufficient, however again using gmic filters

Using this; The eye is about 10 pix across

   

Then gmic Upscale[edge] x8  + a little gmic Sharpen(Gold-Meinel)

   

and the inevitable 60 second video:  https://i.imgur.com/URdP83a.mp4

Edit: a reminder, Image viewers (especially Windows ) and web browsers do smooth an image, Gimp shows true details.