Re: very simple: intersection of zeroes of two functions
From: William Elliot (marsh_at_privacy.net)
Date: 01/27/05
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Date: Wed, 26 Jan 2005 22:50:41 -0800
On Wed, 26 Jan 2005, Alex Hunsley wrote:
> José Carlos Santos wrote:
>> On 26-01-2005 14:26, Alex Hunsley wrote:
>>
>>> Take two functions, say f(x) and g(y) (on reals only).
>>> If I want a function H(x) which has zeroes at the intersection of the
>>> zeroes of f and g, the simplest definition would appear to be:
>>>
>>> H(x) = sqrt(f(x)^2 + g(x)^2)
>>
>> Yes, it makes sense. Of course, you would achieve the same result with
>> H(x) = |f(x)| + |g(x)|,
>>
> sorry, just to clarify, the simpler the expression (computationally) the
> better!
Let Z(x) = 0 if x = 0, = 1 otherwise.
H(x) = Zf(x) + Zg(x)
or if you numerical form of & which is computationally easier than +
H(x) = Zf(x) & Zg(x)
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