The Cauchy Problem for the Laplace Equation and Application to Image Inpainting

Table 1

The error in the reconstruction of 𝑢 and 𝜕𝑢/𝜕𝑛 is evaluated with respect to the number of moments calculated 𝑁∶=1,…,19.

𝑁	𝐸(𝑢)	𝐸(𝜕𝑢/𝜕𝑛)
1	0.4999	2.4994
2	0.1812	0.9058
3	0.0758	0.3792
4	0.0152	0.0761
5	0.0043	0.030
6	0.0006	0.0213
7	0.0001	0.0006
8	0.0	0.0001
9	0.0	0.0
10	0.0	0.0
11	0.0	0.0
12	0.0	0.0
13	0.0	0.0
14	0.0001	0.0026
15	0.0001	0.0221
16	0.0002	0.042
17	0.0019	1.0638
18	0.0769	3.46
19	0.11	52.2134
20	3.0485	1423.61