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EMBED Equation.3 bo’lganda kvadratik yoki parabolik interpolyatsiya deb ataladi.
EMBED Equation.3 (9)
(9) formula uch nuqtadan o’tuvchi parabola tenglamasidir.
Misol. [3,5; 3,7] oraliqda EMBED Equation.3 qadam bilan EMBED Equation.3 funktsiya jadval usulida berilgan Nyutonning birinchi interpolyatsion formulasi yordamida analitik ko’rinishga keltiring.

EMBED Equation.3	3,50	3,55	3,60	3,65	3,70
EMBED Equation.3	33,115	34,813	36,598	38,475	40,447

Qulaylik uchun chekli ayirmalar jadvalini keltiramiz.

xi	EMBED Equation.3	EMBED Equation.3	EMBED Equation.3	EMBED Equation.3	EMBED Equation.3
=3,5	=33,115
		EMBED Equation.3 =1,698
EMBED Equation.3 =3,55	EMBED Equation.3 =34,813		EMBED Equation.3 =0,087
		EMBED Equation.3 =1.785		EMBED Equation.3 =0,005
EMBED Equation.3 =3,6	EMBED Equation.3 =36,598		EMBED Equation.3 =0,092		EMBED Equation.3 = -0,002
		EMBED Equation.3 =1,877		EMBED Equation.3 =0,003
EMBED Equation.3 =3,65	EMBED Equation.3 =38,475		EMBED Equation.3 =0,095
		EMBED Equation.3 =1,972
EMBED Equation.3 =3,7	EMBED Equation.3 =40,447

Jadvalga va (4) ga asosan
EMBED Equation.3
kelib chiqadi.

LABORATORIYA ISHI № 13

Nyutonning ikkinchi interpolyatsion formulasi.

Funktsiyaning ma’lum qiymatlariga ko’ra uning analitik ifodasini topish masalasi, geometrik nuqtai nazardan, EMBED Equation.3 nuqtalar berilganda, bu nuqtalar orqali o’tuvchi egri chiziqni topishni bildiradi (6-chizma).

Berilgan nuqtalardan cheksiz ko’p egri chiziqlar o’tkazish mumkinligi o’quvchiga ravshan bo’lishi kerak. Shunday qilib, EMBED Equation.3 funktsiyaning qiymatlariga ko’ra, uning analitik ifodasini topish masalasi juda ko’p yechimlarga egadir, yani bunday funktsiyalarni cheksiz ko’p tuzish mumkin.
Berilgan nuqtalarda berilgan qiymatlarni qabul qiluvchi istalgan funktsiyani EMBED Equation.3 bilan belgilaymiz. Yuqorida aytib o’tilganidek, EMBED Equation.3 funktsiya istalgancha ko’p bo’lishi mumkin.
Faraz qilaylik, EMBED Equation.3 funktsiya ixtiyoriy bo’lmay, bazi shartlarni qanoatlantirish kerak bo’lsin, unda bu funktsiyani topish anchagina aniq masalaga aylanib qoladi. Ko’pincha EMBED Equation.3 funktsiya darajasi izlanayotgan EMBED Equation.3 funktsiyaning berilgan qiymatlari sonidan bitta kam bo’lgan ko’phad bo’lishi talab qilinadi.
Shunday qilib, biz quyidagi ko’rinishdagi masalaga keldik. EMBED Equation.3 ning EMBED Equation.3 va EMBED Equation.3 qiymatlari uchun shunday EMBED Equation.3 ko’phadni topish kerakki, bu ko’phad n-chi darajali bo’lsin va shartlarni qanoatlantirsin:
EMBED Equation.3 (1)
Boshqacha qilib aytganda, bu erda, berilgan nuqtalarda berilgan qiymatlarni qabul qiluvchi ko’phadni topish masalasi qo’yilgan.