Hisoblash usullari fanidan laboratoriya ishlari

EMBED Equation.3
ko’rinishda bo’ladi. Bu erda a va b lar shu nuqtalarning absissalari. n=2 bo’lganda 3 ta nuqtadan o’tuvchi parabola tenglamasi hosil bo’ladi.


EMBED Equation.3


Eytken sxemasi. Interpolyatsion ko’phadni ko’rish uchun hisoblashlarni soddalashtirish maqsadida Eytken sxemasini qo’llash qulaydir. EMBED Equation.3 orqali EMBED Equation.3 tugunlar yordamida qurilgan EMBED Equation.3 - darajali ko’phadni belgilaymiz.
EMBED Equation.3
formulaga asosan
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
Endi EMBED Equation.3 ifoda EMBED Equation.3 va EMBED Equation.3 lardan qanday qonuniyat bilan tuzilgan bo’lsa, huddi shu qonuniyat bilan EMBED Equation.3 va EMBED Equation.3 yordamida tuzilgan
EMBED Equation.3
ifodani ko’rib chiqamiz. Ko’rinib turibdiki, EMBED Equation.3 ikkinchi darajali ko’phad bo’lib
EMBED Equation.3 , EMBED Equation.3 , EMBED Equation.3
tengliklar o’rinlidir. Demak,
EMBED Equation.3
Shunday qilib, EMBED Equation.3 va EMBED Equation.3 ga birinchi tartibli interpolyatsiyani qo’llab, EMBED Equation.3 ko’phadga ega bo’ldik. Xuddi shu natijani qolgan ikki formuladan ham hosil qila olamiz:
EMBED Equation.3 ,
EMBED Equation.3 ,
bu jarayonni cheksiz davom ettirish mumkin.
Shunday qilib, EMBED Equation.3 ta nuqta yordamida EMBED Equation.3 - darajali interpolyatsion ko’phad ko’rish uchun shu nuqtalarning EMBED Equation.3 tasi yordamida tuzilgan ikkita bir-biridan farqli EMBED Equation.3 - darajali interpolyatsion ko’phadlarga birinchi tartibli interpolyatsiyani qo’llash kerak. Masalan,
EMBED Equation.3
Yuqorida keltirilgan sxema Eytken sxemasi deyiladi. Odatda Eytken sxemasi ning umumiy ko’rinishini topish mumkin emas, balki uning biror EMBED Equation.3 nuqtadagi qiymatini hisoblashda foydalaniladi. Hisoblashlarni 1-jadval shaklida yozish ma’quldir.

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	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

Misol: Qadami EMBED Equation.3 ga teng bo’lgan EMBED Equation.3 ning jadvalidan foydalanib, EMBED Equation.3 ning EMBED Equation.3 nuqtadagi qiymatini topamiz. Hisoblash natijalari 2-jadvalda keltirilgan.


2-jadval

0,68	0,62879	-0,024
0,69	0,63654	-0,014	0,647400
0,70	0,64422	-0,004	0,647292	0,6472488
0,71	0,65183	0,006	0,647264	0,6472808	0,6472626
0,72	0,65938	0,016	0,647300	0,6472424	0,6473038	0,6472679
Sin 0,704=0,64727