Tugunlar orasidagi masofa teng bo’lmaganda Nyuton interpolyatsion formulasi. Bo’lingan chekli ayirmalar



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Bunday masala interpolyasiyalash deyiladi, nuqtalar interpolyatsiya tugunlari deyiladi.

Yuqoridagi shartni qanoatlantiruvchi funktsiya interpolyatsion ko’phad deyilib, bu ko’phadni tuzish uchun ishlatiladigan formulalar interpolyatsion formulalar deyiladi.

Nyutonning ikkinchi interpolyatsion formulasi ham interpolyasiya qadamlari bir-biriga teng bo’lganda yaroqlidir. Nyuton o’zing ikkinchi interpolyatsion formulasini quyidagicha axtaradi.

(2)

Koeffitsentlarni aniqlash huddi oldingidek bo’ladi.



shartdan

shartdan

kelib chiqadi.

shart

va ifodadan





kelib chiqadi.

Bulardan quyidagi rekurent formulani yozish mumkin

(3)

topilganlarni (2) ga olib borib qo’ysak.



(4)

(4) formula Nyutonning ikkinchi interpolyatsion formulasi deyiladi.

Nyutonning ikkinchi interpolyatsion formulasini ham yangi o’zgaruvchilarda ifodalash mumkin.

Formulada belgilash kiritamiz. Unda



formulaga ega bo’lamiz.




X


Variantlar

X0



1

2

3

4

5

Y=

Y=

Y=

Y=

Y=

X0=0.41

Y0=1.5068

Y0=0.4346

Y0=0.0998

Y0=0.9171

Y0=0.6403

0.39

X1=0.46

Y1=1.5841

Y1=0.4954

Y1=0.1439

Y1=0.8961

Y1=0.6782

0.53

X2=0.51

Y2=1.6653

Y2=0.5593

Y2=0.4882

Y2=0.8722

Y2=0.7141

0.60

X3=0.56

Y3=1.7506

Y3=0.6259

Y3=0.5312

Y3=0.8472

Y3=0.5483

0.68

X4=0.61

Y4=1.8404

Y4=0.6989

Y4=0.5728

Y4=0.8196

Y4=0.7810




X5=0.66

Y5=1.9348

Y5=0.7761

Y5=0.6131

Y5=0.7899

Y5=0.8124






X


Variantlar

X0



6

7

8

9

10

Y=

Y=

Y=

Y=

Y=

X0=0,11

Y0=1,1163

Y0=0,1104

Y0=0,1098

Y0=0,9940

Y0=0,3317

0,14

X1=0,16

Y1=1,1735

Y1=0,1514

Y1=0,1593

Y1=0,9872

Y1=0,4000

0,19

X2=0,21

Y2=1,2337

Y2=0,2131

Y2=0,2085

Y2=0,9780

Y2=0,4582

0,29

X3=0,26

Y3=1,2969

Y3=0,2660

Y3=0,5271

Y3=0,9664

Y3=0,5099

0,38

X4=0,31

Y4=1,3634

Y4=0,3203

Y4=0,3051

Y4=0,9523

Y4=0,5568




X5=0,36

Y5=1,4333

Y5=0,3776

Y5=0,3523

Y5=0,9359

Y5=0,6000






X


Variantlar

X0



11

12

13

14

15

Y=

Y=

Y=

Y=

Y=

X0=0.21

Y0=1.2337

Y0=0.2131

Y0=0.2085

Y0=0.9780

Y0=0.4582

0.24

X1=0.26

Y1=1.2969

Y1=0.2660

Y1=0.2571

Y1=0.9664

Y1=0.5099

0.28

X2=0.31

Y2=1.3634

Y2=0.3203

Y2=0.3051

Y2=0.9523

Y2=0.5568

0.39

X3=0.36

Y3=1.4333

Y3=0.3776

Y3=0.3523

Y3=0.9359

Y3=0.6000

0.48

X4=0.41

Y4=1.5068

Y4=0.4346

Y4=0.0998

Y4=0.9171

Y4=0.6403




X5=0.46

Y5=1.5841

Y5=0.4954

Y5=0.4439

Y5=0.8961

Y5=0.6782



X


Variantlar

X0



16

17

18

19

20

Y=

Y=

Y=

Y=

Y=

X0=0.31

Y0=1.3634

Y0=0.3203

Y0=0.3051

Y0=0.9523

Y0=0.5568

0.34

X1=0.36

Y1=1.4333

Y1=0.3776

Y1=0.3523

Y1=0.9359

Y1=0.6000

0.38

X2=0.41

Y2=1.5068

Y2=0.4346

Y2=0.3998

Y2=0.9171

Y2=0.6403

0.49

X3=0.46

Y3=1.5841

Y3=0.4954

Y3=0.4439

Y3=0.8961

Y3=0.6782

0.58

X4=0.51

Y4=1.6653

Y4=0.5593

Y4=0.4882

Y4=0.8722

Y4=0.7141




X5=0.56

Y5=1.7506

Y5=0.6259

Y5=0.5312

Y5=0.8472

Y5=0.7483






X


Variantlar

X0



21

22

23

24

25




Y=

Y=

Y=

Y=

Y=

X0=051

Y0=1.6653

Y0=0.5593

Y0=0.4882

Y0=08722

Y0=0.7141

0.54

X1=0.56

Y1=1.7506

Y1=0.6269

Y1=0.5312

Y1=0.8472

Y1=0.7483

0.58

X2=0.61

Y2=1.8404

Y2=0.9689

Y2=0.5728

Y2=0.8196

Y2=0.7810

0.69

X3=0.66

Y3=1.9348

Y3=0.7761

Y3=0.6131

Y3=0.7899

Y3=0.8124

0.78

X4=0.71

Y4=2.0340

Y4=0.8595

Y4=0.6518

Y4=0.7584

Y4=0.8426




X5=0.76

Y5=2.1353

Y5=0.9504

Y5=0.6889

Y5=0.7248

Y5=0.8718




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