For an newer article on this topic, please read Interpolation Revisited
We are now looking at some serious image sizes. At 400% interpolation, an eight megapixel camera will produce a 30.8 x 46.2 print at 300 PPI. A 12.8 megapixel camera will produce a 38.9 x 58.4 print at the same resolution. This is beyond the size that most photographers will print on a regular basis.
Figures 1 to 5 show the Egret at 400%.
Figures 6 to 10 show the Mojave Green at 400%.
Figures 11 to 15 show the clock at 400%.
Figures 16 to 20 show the doll at 400%.
The conclusions at 400% mirror the 300% conclusions:
At 400% interpolation, the best interpolation method for an image may depend on the image itself.
The best interpolation method may depend on the size of the interpolation. There is relatively little difference between interpolation methods at 200%. However, as the interpolations get larger, the differences between interpolations methods become more noticeable.
So, which method is best? As is generally the case with my responses, the answer is: it depends. These tests show that it depends on the image and the degree of interpolation that is required. Yet, there are other factors that this test did not evaluate. These images where viewed on a monitor at 100% view. This allowed us to evaluate what was happening at the pixel level. Unfortunately, no monitor can perfectly predict how an image will actually print (especially with regard to sharpness). Furthermore, the printer used will most likely make a difference. Papers are another variable. Some papers show better detail than others. Lastly, the intent of the photographer is a major factor. While a landscape photographer will likely want the greatest detail possible, a portrait photographer may not desire such detail (not many of his customers want the image to show every facial imperfection with amazing detail) and may be less concerned about the differences between interpolation methodologies.
These tests are a start. However, if you want the best prints possible, you will need to conduct further tests by making prints on your printer and comparing the results to your needs.