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Ray Sequences of Best Rational Approximants For |x|α
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- Journal:
- Canadian Journal of Mathematics / Volume 49 / Issue 5 / 01 October 1997
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1034-1065
- Print publication:
- 01 October 1997
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- Article
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The 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)} satisfies
In 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.
with numerator degree m and denominator degree n to the function |x|
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.