Numerical integration/Adaptive Simpson's method: Difference between revisions
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'''return''' _quad_asr(f, a, fa, b, fb, tol, whole, m, fm, depth) |
'''return''' _quad_asr(f, a, fa, b, fb, tol, whole, m, fm, depth) |
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Revision as of 22:36, 29 September 2018
Numerical integration/Adaptive Simpson's method is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Lychee (1969)'s Modified Adaptive Simpson's method (doi:10.1145/321526.321537) is a numerical quadrature method that recursively bisects the interval until the precision is high enough.
; Lychee's ASR, Modifications 1, 2, 3
procedure _quad_asr_simpsons(f, a, fa, b, fb)
m := (a + b) / 2
fm := f(m)
h := b - a
return multiple [m, fm, (h / 6) * (f(a) + f(b) + 4*sum1 + 2*sum2)]
procedure _quad_asr(f, a, fa, b, fb, tol, whole, m, fm, depth)
lm, flm, left := _quad_asr_simpsons(f, a, fa, m, fm)
rm, frm, right := _quad_asr_simpsons(f, m, fm, b, fb)
delta := left + right - whole
tol' := tol / 2
if depth <= 0 or tol' == tol or abs(delta) <= 15 * tol:
return left + right + delta / 15
else:
return _quad_asr(f, a, fa, m, fm, tol', left , lm, flm, depth - 1) +
_quad_asr(f, m, fm, b, fb, tol', right, rm, frm, depth - 1)
procedure quad_asr(f, a, b, tol, depth)
fa := f(a)
fb := f(b)
m, fm, whole := _quad_asr_simpsons(f, a, fa, b, fb)
return _quad_asr(f, a, fa, b, fb, tol, whole, m, fm, depth)
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