I think this thread has wandered a bit off topic. To answer the OP's question as best I can:
I agree with the posts so far that you need to look at the average power, and I would choose an amp that can provide what the speaker manufacturer recommends, but to some extent the (average) power of the amp you choose might depend on how you use your speakers.
Someone please correct me if I'm wrong, but this is how I look at it:
The source signal/wave represents how the microphone diaphragm moved when the recording was originally mastered, and as such describes how the cones of your speakers should also move. The Y axis corresponds to the potential difference (voltage) that the amplifier applies to its outputs in an attempt to put the cone where it should be. I like the term potential (difference), it implies there is something to be exploited, rather than a guarantee of the outcome. Now think of the power of the amp as the current it is able to provide at a particular voltage - the degree to which it can guarantee that voltage - in order to get the cone to where it should be - the force as it were, to get the cone moving. Bear in mind a moving coil in a magnet generates resistant force (back EMF) as well as the cone mass inertia and the elastic properties of the cone suspension (did I say off topic? Lol) but on the whole, the greater the force (current) the more closely the cone position will follow the signal. For this reason, upping the power and available current of the amplifier will improve the accuracy (sound quality) of any speaker, which may be particularly noticeable at lower listening volumes, where some much needed force/authority to move the cone may have been lacking. But one can only raise the available current so much before increases cease to have any effect. The speaker is a resistance (a load) which will only draw so much current from the amp (which is why you can play 50w speakers with a 1000w amp at low volumes) but as the volume and hence voltage rises, the power (current x voltage) rises and the ability of the coil to dissipate heat may start to lag behind the heat being generated. This will give distortion and may damage the driver. Also the cone can be driven beyond its limits which will also damage the driver.
So to simplify, an over-specified amp (average power compared with the power rating of the speakers) will give you more accuracy up to the limits of your speakers but you could damage them thermally or physically by turning the volume up too high.
Just to complicate matters, an underpowered amp can also (is probably more likely to?) damage your speakers if it clips and sends nasty discontinuous voltages to your speakers.
That's my take, I look forward to correction from the gurus