Poles and zeros of best rational approximants of |x|

1994 ◽  
Vol 10 (4) ◽  
pp. 469-522 ◽  
Author(s):  
H. Stahl
Keyword(s):  
Rational Approximants ◽  
Poles And Zeros ◽  
Best Rational Approximants

Ray Sequences of Best Rational Approximants For |x|α

1997 ◽  
Vol 49 (5) ◽  
pp. 1034-1065 ◽  
Author(s):  
E. B. Saff ◽  
H. Stahl
Keyword(s):  
Error Function ◽  
Extreme Points ◽  
Rational Approximations ◽  
Rational Approximants ◽  
Convergence Behavior ◽  
Distribution Of Poles ◽  
Poles And Zeros ◽  
Lower Triangle ◽  
Image Position ◽  
Best Rational Approximants

AbstractThe convergence behavior of best uniform rational approximations with numerator degree m and denominator degree n to the function |x|α, α > 0, on [-1, 1] is investigated. It is assumed that the indices (m, n) progress along a ray sequence in the lower triangle of the Walsh table, i.e. the sequence of indices {(m, n)} satisfiesIn addition to the convergence behavior, the asymptotic distribution of poles and zeros of the approximants and the distribution of the extreme points of the error function on [-1, 1] will be studied. The results will be compared with those for paradiagonal sequences (m = n + 2[α/2]) and for sequences of best polynomial approximants.

scholarly journals On the Distribution of Zeros and Poles of Rational Approximants on Intervals

2012 ◽  
Vol 2012 ◽  
pp. 1-21
Author(s):  
V. V. Andrievskii ◽  
H.-P. Blatt ◽  
R. K. Kovacheva
Keyword(s):  
Asymptotic Distribution ◽  
Polynomial Approximation ◽  
Additional Assumption ◽  
Equilibrium Measure ◽  
Distribution Of Zeros ◽  
Rational Approximants ◽  
Bounded Degree ◽  
Asymptotic Distribution Of Zeros ◽  
Best Rational Approximants ◽  
Zeros And Poles

The distribution of zeros and poles of best rational approximants is well understood for the functions , . If is not holomorphic on , the distribution of the zeros of best rational approximants is governed by the equilibrium measure of under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, -values, and poles of best real rational approximants of degree at most to a function that is real-valued, but not holomorphic on . Generalizations to the lower half of the Walsh table are indicated.

scholarly journals Padé approximants as limits of best rational approximants

1974 ◽  
Vol 12 (2) ◽  
pp. 201-204 ◽  
Author(s):  
Charles K Chui ◽  
Oved Shisha ◽  
Philip W Smith
Keyword(s):  
Padé Approximants ◽  
Rational Approximants ◽  
Pade Approximants ◽  
Best Rational Approximants
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