Polynomial Norm
المؤلف:
Borwein, P. and Erdélyi, T.
المصدر:
"Norms on P_n." §1.1.E.3 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag
الجزء والصفحة:
...
13-2-2019
1305
Polynomial Norm
For a polynomial
 |
(1)
|
several classes of norms are commonly defined. The 
-norm is defined as
 |
(2)
|
for 
, giving the special cases
Here, 
is called the polynomial height. Note that some authors (especially in the area of Diophantine analysis) use 
as a shorthand for 
and 
as a shorthand for 
, while others (especially in the area of computational complexity) used 
to denote the 
-norm 
and (Zippel 1993, p. 174).
Another class of norms is the 
-norms, defined by
![||P||_(L_p)=[int_0^(2pi)|P(e^(itheta))|^p(dtheta)/(2pi)]^(1/p)](http://mathworld.wolfram.com/images/equations/PolynomialNorm/NumberedEquation3.gif) |
(6)
|
for 
, giving the special cases
(Borwein and Erdélyi 1995, p. 6).
REFERENCES:
Borwein, P. and Erdélyi, T. "Norms on 
." §1.1.E.3 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, pp. 6-7, 1995.
Zippel, R. Effective Polynomial Computation. Boston, MA: Kluwer, 1993.
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