Дроби | Многочлени | ||||
Nx | Ny | Абсолютна похибка | Відносна похибка | Абсолютна похибка | Відносна похибка |
1 | 1 | 0.33321289914 | 0.33653560644 | 0.33321289915 | 0.33653560644 |
1 | 3 | 0.73677995151 | 1.04635973670 | 0.08595077159 | 0.03314296132 |
1 | 5 | 1.33074173890 | 1.88989205360 | 0.07813929752 | 0.02917129136 |
1 | 7 | 1.62218793880 | 2.30379795360 | 0.07813929752 | 0.02917129136 |
1 | 9 | 1.79019962860 | 2.54240470060 | 0.07813929752 | 0.02917129136 |
2 | 1 | 0.38093142953 | 0.34088982997 | 0.33321289915 | 0.33653560644 |
2 | 3 | 108.52828854000 | 53.79528438600 | 0.03508293819 | 0.01603710670 |
2 | 5 | 11.83751443500 | 7.39333862160 | 0.00603397369 | 0.00249673379 |
2 | 7 | 16.45134666900 | 8.06771331410 | 0.00400187107 | 0.00192186007 |
2 | 9 | 2.05270709570 | 2.91521240740 | 0.00400067177 | 0.00167984100 |
3 | 1 | 0.39983806877 | 0.33697516590 | 0.33321289915 | 0.33653560644 |
3 | 3 | 1.14373906680 | 0.51796639019 | 0.03557770402 | 0.01554997138 |
3 | 5 | 4.67590088140 | 7.12118962440 | 0.00381000491 | 0.00141566619 |
3 | 7 | 11.96976264600 | 16.28514014100 | 0.00033487286 | 0.00012611838 |
3 | 9 | 147.32611065000 | 233.71213864000 | 0.00031603341 | 0.00011626823 |
4 | 1 | 0.41031461388 | 0.34580457911 | 0.33321289915 | 0.33653560644 |
4 | 5 | 0.11547401539 | 0.24612708912 | 0.00362522058 | 0.00135704259 |
4 | 7 | 6.98163079780 | 8.70159328850 | 0.00032007830 | 0.00011789993 |
4 | 9 | 200.89868231000 | 293.47604804000 | 0.00003393168 | 0.00001248529 |
5 | 1 | 0.41657778719 | 0.35108305064 | 0.33321289915 | 0.33653560644 |
5 | 3 | 1.14373906680 | 0.51796639019 | 0.03562571500 | 0.01557095557 |
5 | 5 | 0.34582075015 | 0.67731374632 | 0.00362829375 | 0.00135819298 |
5 | 7 | 0.28787460088 | 0.61359031559 | 0.00032007830 | 0.00011789993 |
5 | 9 | 269.46848274000 | 272.15554826000 | 0.00002340247 | 0.00000860974 |
6 | 1 | 0.42073715224 | 0.35458847656 | 0.33321289915 | 0.33653560644 |
6 | 3 | 1.14373906680 | 0.51796639019 | 0.03562582010 | 0.01557100151 |
6 | 5 | 0.60178232858 | 0.37088347949 | 0.00362800563 | 0.00135808512 |
6 | 7 | 0.01416028441 | 0.02216220490 | 0.00032007830 | 0.00011789993 |
6 | 9 | 28.07739896100 | 54.37392461800 | 0.00002340247 | 0.00000860974 |
7 | 1 | 0.42369817759 | 0.35708396682 | 0.33321289915 | 0.33653560644 |
7 | 3 | 1.14373906680 | 0.51796639019 | 0.03562582720 | 0.01557100461 |
7 | 5 | 0.05427097853 | 0.07817272312 | 0.00362797915 | 0.00135807521 |
7 | 7 | 0.56527796409 | 0.35305480951 | 0.00032007830 | 0.00011789993 |
7 | 9 | 5.01541001920 | 9.82302579570 | 0.00002340247 | 0.00000860974 |
9 | 1 | 0.42763109602 | 0.36039854827 | 0.33321289915 | 0.33653560644 |
9 | 3 | 1.14373906680 | 0.51796639019 | 0.03562582735 | 0.01557100468 |
9 | 5 | 0.05584037058 | 0.06756330821 | 0.00362797928 | 0.00135807526 |
9 | 7 | 0.02959303991 | 0.01731231796 | 0.00032007830 | 0.00011789993 |
9 | 9 | 116.67208874000 | 215.64192761000 | 0.00002340247 | 0.00000860974 |
10 | 1 | 0.42900308940 | 0.36155483560 | 0.33321289915 | 0.33653560644 |
10 | 3 | 1.14373906680 | 0.51796639019 | 0.03562582737 | 0.01557100468 |
10 | 5 | 0.63474784430 | 0.44891954547 | 0.00362797927 | 0.00135807526 |
10 | 7 | 0.15990232197 | 0.20225726009 | 0.00032007830 | 0.00011789993 |
10 | 9 | 0.16799591213 | 0.35807488549 | 0.00002340247 | 0.00000860974 |
13 | 9 | 2.27019124730 | 3.22407892740 | 0.00000208216 | 0.00000077835 |
13 | 13 | 0.00128811535 | 0.00243770956 | 0.00000000485 | 0.00000000187 |
13 | 17 | 0.29511946594 | 0.62903238318 | 0.00000000020 | 0.00000000008 |
16 | 11 | 0.02165218885 | 0.03370435287 | 0.00000007629 | 0.00000003166 |
16 | 16 | 0.00024923150 | 0.00048375231 | 0.00000000051 | 0.00000000021 |
16 | 21 | 0.03300286513 | 0.05765061767 | 0.00000000385 | 0.00000000513 |
19 | 13 | 0.36381363022 | 0.77545055905 | 0.00000000487 | 0.00000000188 |
19 | 19 | 0.00091145851 | 0.00161422039 | 0.00000000459 | 0.00000000169 |
19 | 25 | 1.20763490720 | 1.99359765480 | 0.00000018628 | 0.00000025101 |
22 | 15 | 0.08304117546 | 0.17699811272 | 0.00000000863 | 0.00000000319 |
22 | 22 | 189.14463951000 | 286.92867409000 | 0.00000010621 | 0.00000020835 |
22 | 29 | 61.62582018300 | 108.07586410000 | 0.00001172893 | 0.00000482399 |
25 | 17 | 0.07959936775 | 0.16966207173 | 0.00000005083 | 0.00000006537 |
25 | 25 | 0.65484417000 | 1.08103516540 | 0.00000642809 | 0.00000266219 |
25 | 33 | 5.44702057510 | 10.14281633600 | 0.00060708267 | 0.00082893024 |
Порівняння точності інтерполяції двовимірними многочленами при виборі рівномірно розташованих вузлів і вузлів, що є коренями многочлена Чебишева.
Рівномірний вибір вузлів | Корені многочлена Чебишева | ||||
Nx | Ny | Абсолютна похибка | Відносна похибка | Абсолютна похибка | Відносна похибка |
1 | 1 | 0.00156998281 | 0.27357026415 | 0.00156998281 | 0.27357026414 |
1 | 3 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
1 | 5 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
1 | 7 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
1 | 9 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
2 | 1 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
2 | 3 | 0.00016279695 | 0.01934678422 | 0.00016279695 | 0.01934678422 |
2 | 5 | 0.00016279695 | 0.01934678422 | 0.00016279695 | 0.01934678422 |
2 | 7 | 0.00016279695 | 0.01934678422 | 0.00016279695 | 0.01934678422 |
2 | 9 | 0.00016279695 | 0.01934678422 | 0.00016279695 | 0.01934678422 |
3 | 1 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
3 | 3 | 0.00001909961 | 0.00212953657 | 0.00001768114 | 0.00327712069 |
3 | 5 | 0.00001554767 | 0.00165338068 | 0.00001768113 | 0.00327712068 |
3 | 7 | 0.00001554767 | 0.00165338068 | 0.00001768114 | 0.00327712068 |
3 | 9 | 0.00001554767 | 0.00165338068 | 0.00001768114 | 0.00327712068 |
5 | 1 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
5 | 3 | 0.00001554767 | 0.00165338068 | 0.00001768114 | 0.00327712069 |
5 | 5 | 0.00000013083 | 0.00001313434 | 0.00000008136 | 0.00001508023 |
5 | 7 | 0.00000009942 | 0.00001000142 | 0.00000008136 | 0.00001508022 |
5 | 9 | 0.00000009942 | 0.00001000142 | 0.00000008136 | 0.00001508023 |
7 | 1 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
7 | 3 | 0.00001554767 | 0.00165338068 | 0.00001768114 | 0.00327712069 |
7 | 5 | 0.00000009942 | 0.00001000142 | 0.00000008136 | 0.00001508023 |
7 | 7 | 0.00000000057 | 0.00000005732 | 0.00000000020 | 0.00000003708 |
7 | 9 | 0.00000000040 | 0.00000003789 | 0.00000000020 | 0.00000003707 |
9 | 1 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
9 | 3 | 0.00001554767 | 0.00165338068 | 0.00001768114 | 0.00327712069 |
9 | 5 | 0.00000009942 | 0.00001000142 | 0.00000008136 | 0.00001508023 |
9 | 7 | 0.00000000040 | 0.00000003789 | 0.00000000020 | 0.00000003708 |
9 | 9 | 0.00000000000 | 0.00000000051 | 0.00000000000 | 0.00000000005 |
10 | 1 | 0.00156978338 | 0.27522922659 | 0.00156978338 | 0.27522922658 |
10 | 3 | 0.00001554767 | 0.00165338068 | 0.00001768114 | 0.00327712069 |
10 | 5 | 0.00000009942 | 0.00001000142 | 0.00000008136 | 0.00001508023 |
10 | 7 | 0.00000000040 | 0.00000003789 | 0.00000000020 | 0.00000003707 |
10 | 9 | 0.00000000000 | 0.00000000060 | 0.00000000000 | 0.00000000005 |
13 | 9 | 0.00000000000 | 0.00000000003 | 0.00000000000 | 0.00000000006 |
13 | 13 | 0.00000000000 | 0.00000000009 | 0.00000000000 | 0.00000000001 |
13 | 17 | 0.00000000000 | 0.00000000008 | 0.00000000000 | 0.00000000001 |
16 | 11 | 0.00000000000 | 0.00000000006 | 0.00000000000 | 0.00000000001 |
16 | 16 | 0.00000000000 | 0.00000000061 | 0.00000000000 | 0.00000000001 |
16 | 21 | 0.00000000003 | 0.00000000320 | 0.00000000000 | 0.00000000002 |
19 | 13 | 0.00000000000 | 0.00000000070 | 0.00000000000 | 0.00000000002 |
19 | 19 | 0.00000000010 | 0.00000003900 | 0.00000000000 | 0.00000000003 |
19 | 25 | 0.00000000129 | 0.00000048009 | 0.00000000000 | 0.00000000001 |
22 | 15 | 0.00000000009 | 0.00000003471 | 0.00000000000 | 0.00000000001 |
22 | 22 | 0.00000000199 | 0.00000020550 | 0.00000000000 | 0.00000000003 |
22 | 29 | 0.00000007989 | 0.00003214657 | 0.00000000000 | 0.00000000002 |
25 | 17 | 0.00000000087 | 0.00000033260 | 0.00000000000 | 0.00000000002 |
25 | 25 | 0.00000002863 | 0.00001087848 | 0.00000000000 | 0.00000000002 |
25 | 33 | 0.00000486983 | 0.00184920698 | 0.00000000000 | 0.00000000002 |