(HP-67) Barkers's Equation
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12-06-2019, 06:39 PM
(This post was last modified: 03-21-2021 04:12 PM by Albert Chan.)
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RE: (HP-67) Barkers's Equation
Solving cubic with Cardano's formula, x³ + 3x - 2W = 0
y = ³√(W + √(W²+1)) x = y - 1/y Note: discriminant = W²+1 > 0, we have only 1 real root for x If W<0, y may be hit with subtraction cancellation. We can avoid catastrophic cancellation by solving x'³ + 3x' - 2|W| = 0 x = sign(W) x' Or, we can go for the big |y|: // assumed acot(W) = atan(1/W) y = ³√(W + sign(W) √(W²+1)) = ³√(cot(acot(W)/2)) We still have the cancellation error issue when y ≈ 1 A better non-iterative formula is to use hyperbolics. x = 2 sinh(sinh-1(W)/3) |
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Messages In This Thread |
(HP-67) Barkers's Equation - SlideRule - 12-06-2019, 01:27 PM
RE: (HP-67) Barkers's Equation - Albert Chan - 12-06-2019 06:39 PM
RE: (HP-67) Barkers's Equation - Albert Chan - 12-07-2019, 09:39 PM
RE: (HP-67) Barkers's Equation - Albert Chan - 01-31-2020, 03:38 PM
RE: (HP-67) Barkers's Equation - Mathias Zechmeister - 04-10-2020, 10:34 PM
RE: (HP-67) Barkers's Equation - Albert Chan - 04-11-2020, 03:29 AM
RE: (HP-67) Barkers's Equation - Mathias Zechmeister - 04-11-2020, 10:18 PM
RE: (HP-67) Barkers's Equation - Mathias Zechmeister - 08-10-2020, 08:10 AM
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