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

Сhekli ayirmalar jadvali.

xi

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