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January 6[edit]

How to multiply two numbers faster?[edit]

What is the fastest algorithm of multiply two numbers? I can square any two (or three)-digit number in less than three seconds, but I am not so fast in multiplying numbers. So, I am looking for some methods by which I can also multiply faster like this boy. Britannica User (talk) 03:21, 6 January 2014 (UTC)[reply]

If you have two number A and B, the fastest way is to find the number with the least digits and perform multiplication and addition on the number of the least digits.

Example: A=12345 and B=234

Result = (12345 * 4) + (12345 * 3 * 10) + (12345 * 2 * 100)

If you look at it carefully, you only need to multiple the following

(1) 12345 * 2

(2) 12345 * 3

(3) 12345 * 4

You mean how the little boy does it in the video? He uses mental/virtual soroban/abacus inside his head. He literally imagine performing actions on the soroban/abacus.

See Mental abacus

202.177.218.59 (talk) 04:49, 6 January 2014 (UTC)[reply]

If you can square any number quickly, then compute the product xy as (x² + y² - (x - y)²)/2. (Don't take this seriously.) – b_jonas 14:01, 6 January 2014 (UTC) [reply]

xy=((x+y)/2)²-((x-y)/2)² only requires 2 squares. Bo Jacoby (talk) 01:29, 7 January 2014 (UTC). [reply]

((x+y)²-(x-y)²)/4 avoids having to square a non-integer. MChesterMC (talk) 09:31, 7 January 2014 (UTC) [reply]

Mental math and algorithms are two different things. For "small" numbers, Karatsuba multiplication is the fastest known algorithm, I believe. For very large numbers, the fast Fourier transform method is faster. For mental math, most use the aforementioned abacus method, and there are books written on the subject. Sławomir Biały (talk) 16:13, 6 January 2014 (UTC)[reply]

Simple poles and residue theorem[edit]

Can anyone explain to me why the poles of f(x)=1/(e^x) are simple? Also does anyone know of a proof that the residue of a simple pole is equal to lim(z-c)f(z) as z approaches z? Furthermore does any know how this simplifys to g(c)/h'(c) when f(z) is of the form g(z)/h(z)? Answers really appreciated!! Cheers! — Preceding unsigned comment added by 31.48.32.123 (talk) 20:47, 6 January 2014 (UTC)[reply]

The function

e^{-z}

only has a pole at infinity, and that is an essential singularity, who is saying it has a simple pole? Dmcq (talk) 12:03, 7 January 2014 (UTC)[reply]

In regards to the second question, you can eliminate the pole in the residue integral by multiplying and dividing by

z-c

. Shrinking the size of the contour, one factor comes out as

\lim(z-c)f(z)

, and the other is just the integral of

1/(z-c)

(up to a factor of 2πi). For the third question, write

h(z)=h_{1}(z)(z-c)

. Then

h_{1}(c)=h'(c)

. Sławomir Biały (talk) 13:28, 7 January 2014 (UTC)[reply]

Thank you! This has cleared a lot up for me! Thank you for taking the time to respond to my question! — Preceding unsigned comment added by 86.169.46.80 (talk) 20:32, 7 January 2014 (UTC)[reply]