Is there any rule-of-thumb for choosing amplifier wattage for the given speakers wattage?
Say I have speakers, 100 W (maximum input power) / 6 Ohm each. Is it ok to match them with 44 W (minimum continuous power) / 8 Ohm / channel?
In general, is it ok to hook up large speakers to weak amplifier? Is it ok to hook up small speakers to powerful amplifier?
I've read that speakers should be able to handle twice the wattage of amplifier output. True?
44W at 8 Ohm means delivering 2.3A at 18.8V RMS. Now assuming that the 2.3A can also be delivered at lower voltages (note: that isn't self-evident since it means a larger maximum voltage drop across the power transistors), at 6 ohm you have just 33W. The speaker can do 100W. That's fine, right?
Once the amplifier starts clipping, a large ratio of the output power will go through the tweeter (assuming a multi-way speaker). For HiFi speakers, that tends to be a bad idea.
So when working with small amps, you need to make sure that the highest speaker alone is already rated for the respective RMS power the amp can deliver. Which means significantly oversizing the speaker in which case you are even more likely to overdrive your amp by accident.
So usually it makes more sense to rather overdimension the amp somewhat: that way the speaker starts sounding bad before the amp goes into overdrive.
Basically the worst case to deal with is a feedback loop. Usually the results are less awful when their output is limited by the speaker rather than the amp.
So you pick the speakers of sufficient size for purpose/venue and then pick an amp that will not overdrive while feeding those speakers for this purpose/venue. Unless the speakers are seriously oversized for purpose/venue, this makes it preferable to dimension the amp rather larger than smaller than the speaker.
Note that this is mostly true for HiFi speakers and still reasonably true for PA systems. Instrument cabinets and amps are a different problem of matching, and valve amps as opposed to solid-state amps are totally different since their limiting action is quite different from the hard clipping of a solid-state amp.
