An Integral Equations Method for the Cauchy Problem Connected with the Helmholtz Equation

Table 2

Regularization parameter 𝛼 and errors for Example 1 of Case 1 with 𝑘=8.

Noise	𝛼	‖𝑈^𝛿𝛼(𝛿)−𝑢‖𝐿2(∑)	‖𝑉^𝛿𝛼(𝛿)−𝜕𝑛𝑢‖𝐿2(∑)/‖𝜕𝑛𝑢‖𝐿2(∑)
0	3.36×10^−16	9×10^−3	4.25×10^−2
0.001	1.16×10^−6	3.56×10^−2	8.07×10^−2
0.01	3.14×10^−5	5.13×10^−2	1.07×10^−1
0.03	2.85×10^−4	5.24×10^−2	1.19×10^−1