Aberth Method
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Aberth method, or Aberth Ehrlich method, named after Oliver Aberth and Louis W. Ehrlich, is a root-finding algorithm for simultaneous approximation of all the roots of a univariate polynomial. The fundamental theorem of algebra states that for each polynomial with complex coefficients there are as many roots as the degree of the polynomial. More specifically, each polynomial of degree n is identical to a product of n linear polynomials. The fundamental theorem in…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Aberth method, or Aberth Ehrlich method, named after Oliver Aberth and Louis W. Ehrlich, is a root-finding algorithm for simultaneous approximation of all the roots of a univariate polynomial. The fundamental theorem of algebra states that for each polynomial with complex coefficients there are as many roots as the degree of the polynomial. More specifically, each polynomial of degree n is identical to a product of n linear polynomials. The fundamental theorem in itself does not offer an efficient numerical procedure to compute those roots. Numerical algorithms that approximate all roots at once are the Weierstrass method and the Aberth Ehrlich method.