Three-Point Hyperbolic Extrapolation To Solve Equations.

by M. L. Juncosa

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Three-point parabolic extrapolation to iteratively solve real or complex, algebraic or transcendental equations has been proposed by D. E. Muller and used frequently on automatic computers, particularly in determination of eigenvalues of matrices. It is suggested here that three-point equilateral hyperbolic extrapolation enjoys the same reasons for adoption as parabolic extrapolation, but has the added advantages of avoiding at each iteration a square root determination, a sign determination, and the need to guard against the possibility of being thrust into the complex domain when seeking real roots of real equations. It is also shown that the order of convergence is the same as that of parabolic extrapolation

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