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The Quarterly Journal of Mechanics and Applied Mathematics 1957 10(1):122-128; doi:10.1093/qjmam/10.1.122
© 1957 by Oxford University Press
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WIDENING THE APPLICABILITY OF LIN'S ITERATION PROCESS FOR DETERMINING QUADRATIC FACTORS OF POLYNOMIALS

J. W. HEAD {dagger}

If an approximation is known to a real or complex root of an algebraic equation, the root can be determined from two applications of Lin's process by an adaptation of Steffensen's device (Aitken's {delta}2-process), whether Lin's process is convergent or divergent, provided that the divergence is not too violent and the roots of the algebraic equation are sufficiently well separated. The basic principle used is that for a sufficiently close starting approximation and a real or complex linear divisor, successive approximations have their first differences in geometric progression. The question of finding a suitable starting approximation is not considered. Two numerical examples, one with real roots and one with complex roots, are discussed fully.


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