scholarly journals The Direct and Converse Theorems for Best Approximation of Algebraic Polynomial in Lp, α (X)

2021 ◽  
Vol 1879 (3) ◽  
pp. 032010
Author(s):  
Alaa Adnan Auad ◽  
Mohammed Hamad Fayyadh
Keyword(s):  
Best Approximation ◽  
Algebraic Polynomial ◽  
Converse Theorems

Classical Approximation

1995 ◽  
Author(s):  
Marek A. Kowalski ◽  
Krzystof A. Sikorski ◽  
Frank Stenger
Keyword(s):  
20Th Century ◽  
Uniform Approximation ◽  
Best Approximation ◽  
Inner Product ◽  
Normed Spaces ◽  
Remez Algorithm ◽  
Best Uniform Approximation ◽  
Converse Theorems ◽  
Inner Product Spaces ◽  
Finite Dimensional

In this chapter we acquaint the reader with the theory of approximation of elements of normed spaces by elements of their finite dimensional subspaces. The theory of best approximation was originated between 1850 and 1860 by Chebyshev. His results and ideas have been extended and complemented in the 20th century by other eminent mathematicians, such as Bernstein, Jackson, and Kolmogorov. Initially, we present the classical theory of best approximation in the setting of normed spaces. Next, we discuss best approximation in unitary (inner product) spaces, and we present several practically important examples. Finally, we give a reasonably complete presentation of best uniform approximation, along with examples, the Remez algorithm, and including converse theorems about best approximation. The goal of this section is to present some general results on approximation in normed spaces.

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

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