Gauss Lucas theorem：SOME APPLICATIONS OF THE GAUSS
SOME APPLICATIONS OF THE GAUSS
A refinement of the Gauss–Lucas theorem (after W.P. ...
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The following theorem by Gauss and rediscovered by Lucas describes a beautiful relationship between the roots of a polynomial and the roots of its derivative.
Gauss
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Theorem. Let P be a non-constant polynomial in C. Then all zeroes of its derivative P′ belong to the convex hull of the set of zeroes of P.
Gauss
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Gauss-Lucas theorem proof ... The Gauss-Lucas Theorem states that: All the critical points of a non-constant polynomial f (i.e. the roots of f′ ) ...
Gauss–Lucas theorem
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Mathematics
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The theorem states that the roots of P' all lie within the convex hull of the roots of P, that is the smallest convex polygon containing the ...
The Gauss–Lucas Theorem
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The Gauss–Lucas theorem says that for any complex poly- nomial , the roots of the derivative ′ lie in the convex hull of the roots of .
Understanding a proof of Gauss
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According to a proof of Gauss-Lucas theorem from wikipedia, a logarithmic derivative of polynomial P(z) is P′(z)P(z)=n∑i=11z−zi=n∑i=1¯z−¯zi| ...
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[2112.00110] The Gauss
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Abstract:The Gauss-Lucas theorem says that for any complex polynomial P, the roots of the derivative P' lie in the convex hull of the roots ...
說明
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