I found that the suggested method of resizing image for blur imitation makes output look very pixelated for very large values of sigma like 25 or more. So I finally came to an idea of downscale-blur-enlarge, which makes very nice result (almost indistinguishable from simple blur with large sigma):
# plain slow blur
convert -blur 0x25 sample.jpg blurred_slow.jpg
# much faster
convert -scale 10% -blur 0x2.5 -resize 1000% sample.jpg blurred_fast.jpg
On my i5 2.7Ghz it shows up to 10x speed up.
https://stackoverflow.com/questions/35649413/imagemagick-looking-for-a-fast-way-to-blur-an-image