Solve a system of two equations in which the existence of ln(α/(α+β)) function makes some limitations in iterations of the Newton-Raphson method.

Rihanna Bentley

Rihanna Bentley

Answered question

2022-11-19

Solve a system of two equations in which the existence of l n ( α α + β ) function makes some limitations in iterations of the Newton-Raphson method.
{ l n ( α α + β ) c s 1 + i A c i ( α i ( α + β ) i ) l n ( β α + β ) c s 1 + i A c i ( β i ( α + β ) i )

Answer & Explanation

hitturn35

hitturn35

Beginner2022-11-20Added 20 answers

Put: X = log ( α α + β ) = log ( 1 1 + β α )
Then working in terms of X will ensure that the logarithm is always well defined. You then need to define another independent variable Y such that a linarization of Y in terms of small changes in α and β does not become almost linearly dependent on the way the change in X depends on small changes in α and β. Since X depends on the ratio of α and β, you can choose Y to be a function of the product of α and β, so:
Y = α β
might work well, at least you'll have elminated two potential problems with Newton-Raphson.
Aron Heath

Aron Heath

Beginner2022-11-21Added 3 answers

We can simply substitute α by a 2 and β by b 2 .

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