Complex Chebyshev approximation with the local Haar condition

University of Manchester Best Chebyshev Approximation by Families of Odes with a Xed Initial Condition Best Chebyshev Approximation by Families of Odes with a Xed Initial Condition

Best Chebyshev approximation of real-valued data is treated by approximations obtained from solutions of parameter dependent initial value problems in ordinary diierential equations, in which the initial conditions are speciied. The problem is a modiied form of the problem treated by the authors in 9], 10], and 11]. The xing of the initial condition at t = a requires that approximation be carri...

Near-Circularity of the Error Curve In Complex Chebyshev Approximation

Let f(z) be analytic on the unit disk, and let p*(z) be the best (Chebyshev) polynomial approximation to f(z) on the disk of degree at most n. It is observed that in typical problems the “error curve,” the image of the unit circle under (f p*)(z), often approximates to a startling degree a perfect circle with winding number n + 1. This phenomenon is approached by consideration of related proble...

Real vs Complex Rational Chebyshev Approximation on an Interval

Real VS. Complex Rational Chebyshev Approximation on an Interval

I f f E C[-I, I] is real-valued, let Er( f ) and E'( f ) be the errors in best approximation to f in the supremum norm by rational functions of type ( m , n ) with real and complex coefficients, respectively. It has recently been observed that E'( f ) < Er( f ) can occur for any n > 1, but for no n 1 is it known whether y,,,, = inf, E'( f ) / E r ( f ) is zero or strictly positive. Here we show...

Discrete linear Chebyshev approximation

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