Applied Mathematics > Numerical Methods > Root-Finding >

Maehly's Procedure

A method for finding roots which defines

P_j(x)=(P(x))/((x-x_1)...(x-x_j)),
(1)

so the derivative is

P_j^'(x)=(P^'(x))/((x-x_1)...(x-x_j))-(P(x))/((x-x_1)...(x-x_j))sum_(i=1)^j(x-x_i)^(-1).
(2)

One step of Newton's method can then be written as

x_(k+1)=x_k-(P(x_k))/(P^'(x_k)-P(x_k)sum_(i=1)^(j)(x_k-x_i)^(-1)).
(3)

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