Hisoblash usullari fanidan laboratoriya ishlari

Nyutonning birinchi interpolyatsion formulasi. Nyutonning birinchi interpolyatsion formulasini keltirib chiqarish uchun chekli ayirmalar tushunchasi kiritiladi. Bunda interpolyatsiya qadamlari bir-biriga teng deb hisoblanadi.
Birinchi tartibli chekli ayirma deganda EMBED Equation.3 tushuniladi. Huddi shuningdek, ikkinchi tartibli chekli ayirma deganda

EMBED Equation.3

amallar tushuniladi.

Amaliy jihatdan chekli ayirmalar hisoblash uchun chekli ayirmalar jadvalidan foydalanilgan ma’qul. Bu jadval quyidagicha.


Chekli ayirmalar jadvali.

xi	EMBED Equation.3	EMBED Equation.3	EMBED Equation.3	EMBED Equation.3	EMBED Equation.3	EMBED Equation.3
		EMBED Equation.3
EMBED Equation.3	EMBED Equation.3		EMBED Equation.3
		EMBED Equation.3		EMBED Equation.3
EMBED Equation.3	EMBED Equation.3		EMBED Equation.3		EMBED Equation.3
		EMBED Equation.3		EMBED Equation.3		EMBED Equation.3
EMBED Equation.3	EMBED Equation.3		EMBED Equation.3		EMBED Equation.3
		EMBED Equation.3		EMBED Equation.3
EMBED Equation.3	EMBED Equation.3		EMBED Equation.3
		EMBED Equation.3
EMBED Equation.3	EMBED Equation.3

EMBED Equation.3 (1)

Nyuton o’zining birinchi interpolyatsion formulasini quyidagicha axtaradi.
EMBED Equation.3 (2)
(2) interpolyatsion formulaning noma’lum EMBED Equation.3 koeffitsientlarini aniqlasak, interpolyatsion formula yozilgan bo’ladi. Buning uchun quyidagi shartlardan foydalanamiz.
EMBED Equation.3 shartdan EMBED Equation.3 ,
EMBED Equation.3 shartdan EMBED Equation.3 .
Bundan EMBED Equation.3 bo’lgani uchun, EMBED Equation.3 bo’ladi.
EMBED Equation.3 shartdan va EMBED Equation.3 bo’lgani uchun
EMBED Equation.3
tenglikka ega bo’lamiz. Bu erdan EMBED Equation.3 ni topamiz:
EMBED Equation.3
Va hakoza bu jarayonni davom qildirsak
EMBED Equation.3 , EMBED Equation.3 (3)
umumiy formulaga ega bo’lamiz.
Topilgan a_i larni (2) formulaga qo’ysak ushbu
EMBED Equation.3 (4)
formulaga ega bo’lamiz. Bu formulaga Nyutonning birinchi interpolyatsion formulasi deyiladi.
Ushbu
EMBED Equation.3 (5)
dan foydalanib, (4) formulada h ni 0 ga intiltirsak ushbu

EMBED Equation.3 (6)

(6) bizga ma’lum bo’lgan Teylor qatori.
Demak, Nyutonning birinchi interpolyatsion formulasida interpolyatsiya qadamini nolga intiltirib limitga o’tsak Teylor qatori kelib chiqar ekan.
Agar (4) formulaning faqat ikki hadini olsak, kvadratik interpolyatsiya deyiladi.
Nyutonning birinchi interpolyatsion formulasini yangi o’zgaruvchi kiritib quydagicha yozish mumkin.
EMBED Equation.3 yangi o’zgaruvchi kiritamiz. U holda
EMBED Equation.3
formulani hosil qilamiz.
EMBED Equation.3
Nyutonning interpolyatsion formulasidan EMBED Equation.3 bo’lsa, chiziqli interpolyatsiya deb aytiladi.
EMBED Equation.3 (7)
EMBED Equation.3
bo’lgani uchun (7) ni quydagicha yozish mumkin
EMBED Equation.3 . (8)
(8) formula ikki nuqtadan o’tuvchi to’g’ri chiziq tenglamasidir.