168
I. P. Markov and M. V. Markina
Fig. 11.13 Total number of integrand evaluations for 1 ≤ ω ≤ 1000 and err(I 2 ) ≤ 1 × 10 −10
and depict it versus frequency 1 ≤ ω ≤ 1000 in Fig. 11.14. From ω ≥ 100 η steadily
increases from 1 to almost 25 for ω ≈ 1000, meaning that for ω ≈ 1000 our procedure
requires almost 25 times less integrand evaluations than GL for err(I 2 ) ≤ 1 × 10
−10 .
Total numbers of integrand evaluations with our procedure are relatively close for
all considered orders of underlining EW method.
We find it is advantageous to use low order (N = 5 or 6, for example) of EW method
and larger number of subintervals of integration than high order of EW method with
lesser number of subintervals since solving our (N + 1) × (N + 1) complex-valued
general linear system requires no less than O((N + 1)
3
) floating-point operations.
Fig. 11.14 Performance coefficient η for 1 ≤ ω ≤ 1000 and err(I 2 ) ≤ 1 × 10 −10
I. P. Markov and M. V. Markina
Fig. 11.13 Total number of integrand evaluations for 1 ≤ ω ≤ 1000 and err(I 2 ) ≤ 1 × 10 −10
and depict it versus frequency 1 ≤ ω ≤ 1000 in Fig. 11.14. From ω ≥ 100 η steadily
increases from 1 to almost 25 for ω ≈ 1000, meaning that for ω ≈ 1000 our procedure
requires almost 25 times less integrand evaluations than GL for err(I 2 ) ≤ 1 × 10
−10 .
Total numbers of integrand evaluations with our procedure are relatively close for
all considered orders of underlining EW method.
We find it is advantageous to use low order (N = 5 or 6, for example) of EW method
and larger number of subintervals of integration than high order of EW method with
lesser number of subintervals since solving our (N + 1) × (N + 1) complex-valued
general linear system requires no less than O((N + 1)
3
) floating-point operations.
Fig. 11.14 Performance coefficient η for 1 ≤ ω ≤ 1000 and err(I 2 ) ≤ 1 × 10 −10