Multiple Root


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multiple root

[′məl·tə·pəl ′rüt]
(mathematics)
A polynomial ƒ(x) has c as a multiple root if (x-c) n is a factor for some n > 1. Also known as repeated root.

Multiple Root

 

A multiple root of the polynomial

f(x) = aoxn + a1xn-1 + … + an

is a number c such that f(x) is divided without remainder by the binomial (x—c) raised to the second or higher degree; c is called a root of multiplicity k iff(x) is divided by (x—c)k but not by (x—c)k+l. A root of multiplicity k of the polynomial f(x) is also a root of all the derivatives of the polynomial up to and including the derivative of order (k — 1), that is, of the polynomials f’(x), f”(x), & ,f(k-1)(x). A multiple root of the polynomial f(x) is also called a multiple root of the equation f(x) = 0.

References in periodicals archive ?
In section 2, we discuss the Fixed Point Modified Generalized Newton-Raphson (FPMGNR) Method for multiple roots whereas in section 3, we compare FPMGNR Method for multiple roots with the other methods considered in this paper through some numerical examples.
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They cover topics in real and complex number complexity theory; the real solving of algebraic varieties with intrinsic complexity; the complexity and geometry of numerically solving polynomial systems; multiplicity hunting and approximating multiple roots of polynomial systems; the intrinsic complexity of elimination problems in effective algebraic geometry; and Newton iteration, conditioning, and zero counting.
Sormani, Some variants of Newton's method with third order convergence and multiple roots, J.
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The Nights has multiple roots from different cultures and its content, that might not be exclusively Oriental, is an issue for many scholars.

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