Monotone Data Visualization Using Rational Trigonometric Spline Interpolation

Table 8

Numerical values corresponding to Figure 8.

(𝑥𝑖,𝑦𝑗)	1	2	3	4	5	6
Numerical values of 𝐹^𝑥𝑖,𝑗
1	1.0279	0.4623	0.2308	0.1322	0.0843	0.0581
2	0.8047	0.4778	0.2939	0.1928	0.1341	0.0979
3	0.6119	0.4581	0.3270	0.2350	0.1731	0.1312
4	0.4778	0.4012	0.3180	0.2473	0.1928	0.1521
5	0.3889	0.3466	0.2939	0.2428	0.1987	0.1627
6	0.3168	0.2966	0.2667	0.2326	0.1991	0.1689
Numerical values of 𝐹^𝑦𝑖,𝑗
1	1.0279	0.8047	0.6119	0.4778	0.3889	0.3168
2	0.4623	0.4778	0.4581	0.4012	0.3466	0.2966
3	0.2308	0.2939	0.3270	0.3180	0.2939	0.2667
4	0.1322	0.1928	0.2350	0.2473	0.2428	0.2326
5	0.0843	0.1341	0.1731	0.1928	0.1987	0.1991
6	0.0581	0.0979	0.1312	0.1521	0.1627	0.1689
Numerical values of 𝛽𝑖,𝑗
1	13.4612	11.8021	10.5579	9.7618	9.2601	—
2	13.9316	11.8084	10.8374	10.3699	10.1191	—
3	13.8377	12.7622	11.9437	11.4236	11.0979	—
4	13.4933	12.9563	12.4102	11.9764	11.6602	—
5	13.2255	12.9325	12.5819	12.2566	11.9879	—
6	—	—	—	—	—	—
Numerical values of 𝛾𝑖,𝑗
1	10.5388	12.1979	13.4421	14.2382	14.7399	—
2	10.5932	11.3237	12.0568	12.6377	13.0617	—
3	10.8043	11.1752	11.6161	12.0237	12.3602	—
4	10.9824	11.1929	11.4696	11.7539	12.0121	—
5	10.7745	11.0675	11.4181	11.7434	12.0121	—
6	—	—	—	—	—	—
Numerical values of 𝛽𝑖,𝑗
1	13.4612	13.9316	13.8377	13.4933	13.2255	—
2	11.8021	11.8084	12.7622	12.9563	12.9325	—
3	10.5579	10.8374	11.9437	12.4102	12.5819	—
4	9.7618	10.3699	11.4236	11.9764	12.2566	—
5	9.2601	10.1191	11.0979	11.6602	11.9879	—
6	—	—	—	—	—	—
Numerical values of 𝛾𝑖,𝑗
1	10.5388	10.5932	10.8043	10.9824	10.7745	—
2	12.1979	11.3237	11.1752	11.1929	11.0675	—
3	13.4421	12.0568	11.6161	11.4696	11.4181	—
4	14.2382	12.6377	12.0237	11.7539	11.7434	—
5	14.7399	13.0617	12.3602	12.0121	12.0121	—
6	—	—	—	—	—	—
Numerical values of 𝛽𝑖,𝑗+1
1	13.7691	12.3176	11.3888	10.8035	10.4245	—
2	13.7765	12.6436	12.0982	11.8056	11.6334	—
3	14.8893	13.9343	13.3275	12.9476	12.7025	—
4	15.1157	14.4785	13.9724	13.6036	13.3401	—
5	15.0879	14.6788	14.2994	13.9859	13.7398	—
6	—	—	—	—	—	—
Numerical values of 𝛾𝑖,𝑗+1
1	13.2144	14.5622	15.4247	15.9682	16.3201	—
2	12.2673	13.0616	13.6908	14.1502	14.4789	—
3	12.1065	12.5841	13.0257	13.3902	13.6766	—
4	12.1257	12.4254	12.7334	13.0131	13.2509	—
5	11.9898	12.3697	12.7220	13.0131	13.2416	—
6	—	—	—	—	—	—
Numerical values of 𝛽𝑖+1,𝑗
1	7.0627	9.6496	12.0876	13.2188	13.7521	—
2	6.8759	8.4746	10.6260	11.9816	12.7945	—
3	7.0547	8.2958	10.0152	11.2619	12.1246	—
4	7.2590	8.4154	9.8191	10.8928	11.7015	—
5	7.4425	8.6142	9.8100	10.7305	11.4556	—
6	—	—	—	—	—	—
Numerical values of 𝛾𝑖+1,𝑗
1	13.2144	12.2673	12.1065	12.1257	11.9898	—
2	14.5622	13.0616	12.5841	12.4254	12.3697	—
3	15.4247	13.6908	13.0257	12.7334	12.7220	—
4	15.9682	14.1502	13.3902	13.0131	13.0131	—
5	16.3201	14.4789	13.6766	13.2509	13.2416	—
6	—	—	—	—	—	—