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

Table 1

Values of 𝑁^{−𝑞−2𝑝−1}max_{𝑥∈[−0.5,0.5]}|𝜑_{𝑁,𝑞,𝑝}(𝑓,𝑥)| (see (38)) for 𝑁=1024, 𝑞+2𝑝=8 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=2	𝑞=4	𝑞=6	𝑞=8
𝑎=1/10	1.5⋅10^−30	4.6⋅10^−34	1.2⋅10^−37	3.9⋅10^−41
𝑎=1	1.2⋅10^−27	3.9⋅10^−29	1.1⋅10^−30	3.3⋅10^−32
𝑎=10	8.0⋅10^−26	2.5⋅10^−25	6.8⋅10^−25	2.2⋅10^−24
𝑎=30	1.3⋅10^−24	3.7⋅10^−23	9.0⋅10^−22	2.6⋅10^−22
𝑎=50	9.7⋅10^−25	7.6⋅10^−23	5.1⋅10^−21	4.1⋅10^−19