Uniform approximation of continuous functions by rational functions

1970 ◽  
Vol 84 (1) ◽  
pp. 375-386 ◽  
Author(s):  
Gaetano Fichera
Keyword(s):  
Uniform Approximation ◽  
Rational Functions ◽  
Continuous Functions ◽  
Approximation Of Continuous Functions

scholarly journals Uniform approximation by (quantum) polynomials

2011 ◽  
Vol 11 (3&4) ◽  
pp. 215-225
Author(s):  
Andrew Drucker ◽  
Ronald de Wolf
Keyword(s):  
Approximation Theory ◽  
Uniform Approximation ◽  
Quantum Algorithms ◽  
Continuous Functions ◽  
Quantum Phase ◽  
Phase Estimation ◽  
Classical Theorem ◽  
Quantitative Version ◽  
Quantum Counting ◽  
Approximation Of Continuous Functions

We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectively on quantum counting and on quantum phase estimation.

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