Determines a zero of a 1D function in a given interval. The function has to be continuous and has to have different signs at the end points of the interval. Details
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accuracy controls the accuracy of the zero determination. The default is 1E - 8. |
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start is the leftmost point of the interval. The default is 0.0. |
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end is the rightmost point of the interval. The default is 0.0. |
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formula is a string describing the function. |
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zero is the determined zero of formula. zero is a good approximation only for the exact value. |
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f(zero) is the function value at the point given by zero. The answer should be very close to zero. |
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ticks is the time effort for the whole calculation of the function values in milliseconds. |
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When start > end, the application interprets it as an error condition. The function values at the points start and end must have different signs to guarantee the existence of a zero in (start,end). |
Given the function
f(x)
with
f(a)*f(b) < 0.
Ridders method determines
c = (a + b)/2
and calculates the new guess
The triplets start, , and end are the base for the new iteration, depending on whether
or
The algorithm stops, if |a b| < accuracy
Ridders method is very fast and reliable.
Ridders method is a generalization of the depicted estimation of a zero, as shown in the following illustration.