scholarly journals Uniform approximation by polynomials with integer coefficients

2016 ◽  
Vol 36 (4) ◽  
pp. 489 ◽  
Author(s):  
Artur Lipnicki
Keyword(s):  
Uniform Approximation ◽  
Integer Coefficients ◽  
Approximation By Polynomials

scholarly journals A note on uniform approximation of functions having a double pole

2014 ◽  
Vol 17 (1) ◽  
pp. 233-244
Author(s):  
Ionela Moale ◽  
Veronika Pillwein
Keyword(s):  
Symbolic Computation ◽  
Uniform Approximation ◽  
Classical Problem ◽  
Type Equation ◽  
Elliptic Functions ◽  
Double Pole ◽  
Approximation Of Functions ◽  
Best Uniform Approximation ◽  
Approximation By Polynomials ◽  
Low Degrees

AbstractWe consider the classical problem of finding the best uniform approximation by polynomials of$1/(x-a)^2,$where$a>1$is given, on the interval$[-\! 1,1]$. First, using symbolic computation tools we derive the explicit expressions of the polynomials of best approximation of low degrees and then give a parametric solution of the problem in terms of elliptic functions. Symbolic computation is invoked then once more to derive a recurrence relation for the coefficients of the polynomials of best uniform approximation based on a Pell-type equation satisfied by the solutions.

Uniform approximation by polynomials in two functions

1989 ◽  
Vol 284 (4) ◽  
pp. 529-535 ◽  
Author(s):  
A. G. O'Farrell ◽  
K. J. Preskenis
Keyword(s):  
Uniform Approximation ◽  
Approximation By Polynomials
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