On a Fast Convergence of the Rational-Trigonometric-Polynomial Interpolation

Table 3

Values of 𝑁^{−2𝑝−𝑞−2}max_{𝑥∈[−0.5,0.5]}|𝜑_{𝑁,𝑞,𝑝}(𝑓,𝑥)| (see (57)) for 𝑁=1024, 𝑞+2𝑝=7 and for function (68). Parameters 𝜏_𝑘 are the roots of the associated Laguerre polynomials 𝐿^𝑞_𝑝(𝑥).

	𝑝=3	𝑝=2	𝑝=1	𝑝=0
	𝑞=1	𝑞=3	𝑞=5	𝑞=7
𝑎=1/10	4.0⋅10^−28	2.0⋅10^−31	4.8⋅10^−35	7.1⋅10^−39
𝑎=1	4.0⋅10^−26	1.9⋅10^−27	4.3⋅10^−29	6.3⋅10^−31
𝑎=10	6.6⋅10^−25	2.3⋅10^−24	4.5⋅10^−24	6.0⋅10^−24
𝑎=30	8.6⋅10^−24	2.3⋅10^−22	3.7⋅10^−21	4.1⋅10^−20
𝑎=50	6.0⋅10^−24	4.3⋅10^−22	1.9⋅10^−20	5.5⋅10^−19