Simple Question: gradient function Formula
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Santino M
el 2 de Feb. de 2015
in the following line, x is a 200 element column vector, h is a scalar eg.say 20 or 30
a = gradient(x,h)
can you please tell how 'a' is computed from x and h? Thanks in advance
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Roger Stafford
el 2 de Feb. de 2015
For 2 <= k <= 199, the computation is a central difference:
a(k) = (x(k+1)-x(k-1))/(2*h)
However, for the two endpoints it is:
a(1) = (x(2)-x(1))/h
a(200) = (x(200)-x(199))/h
In case h is a vector of the same length as x, then it becomes a divided difference:
a(k) = (x(k+1)-x(k-1))/(h(k+1)-h(k-1))
and
a(1) = (x(2)-x(1))/(h(2)-h(1))
a(200) = (x(200)-x(199))/(h(200)-h(199))
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