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

Table 2

Values of max_{𝑥∈[−0.5,0.5]}|𝑟^𝑝_𝑁,𝑞(𝑓,𝑥)| (see (26)) 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	1.2⋅10^−30	3.9⋅10^−34	1.2⋅10^−37	3.9⋅10^−41
𝑎=1	9.8⋅10^−28	3.3⋅10^−29	9.9⋅10^−31	3.3⋅10^−32
𝑎=10	6.3⋅10^−26	2.1⋅10^−25	6.4⋅10^−25	2.1⋅10^−24
𝑎=30	1.0⋅10^−24	3.1⋅10^−23	8.5⋅10^−22	2.6⋅10^−22
𝑎=50	7.8⋅10^−25	6.4⋅10^−23	4.8⋅10^−21	4.0⋅10^−19