1.10, due on September 24
Difficult:
I actually had a hard time understanding the algorithm for multiplying two numbers digit-by-digit at first. But thinking about it more, I was able to understand it. One thing I still do not understand is how eqn. (1.47) only has 3 long multiplications - it looks like it has 5. Do the multiplications by factors of 10 not count?
Reflective:
I thought it was amazing, the reworking of equations that they do in order to make the algorithms a tiny bit faster -- for example, Strassen discovered a way to do matrix multiplication using 7 multiplications rather than 8, which reduced the O of the algorithm by <.2 on large matrices. But I think it is amazing, because on large matrices that can result in matrix multiplication in half the time! Pretty cool.
I actually had a hard time understanding the algorithm for multiplying two numbers digit-by-digit at first. But thinking about it more, I was able to understand it. One thing I still do not understand is how eqn. (1.47) only has 3 long multiplications - it looks like it has 5. Do the multiplications by factors of 10 not count?
Reflective:
I thought it was amazing, the reworking of equations that they do in order to make the algorithms a tiny bit faster -- for example, Strassen discovered a way to do matrix multiplication using 7 multiplications rather than 8, which reduced the O of the algorithm by <.2 on large matrices. But I think it is amazing, because on large matrices that can result in matrix multiplication in half the time! Pretty cool.
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