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chiziqli algebraik tenglamalar sistamasini (chats) yechishning taqribiy usullari. zeydel usuli zeydel usuli faraz qilaylik quyidagi sistema berilgan bo’lsin: , , (3.1) ……………………….. . takribiy yechish usullari orqali sistemaning yechimini aniqlaymiz (ya’ni shunday usullarni qo’llash lozimki hisoblashlarni yaxlitlanmasdan yechim ni ma’lum bir aniqlikda topish lozim). agar (3.1) ning noma’lumlari soni ko’p bo’lsa, uning aniq yechimini topish qiyinlashadi. bunday hollarda sistemaning yechimlarini topish uchun taqribiy usullardan foydalaniladi. bu esa yechimni topish vaqtini 20-30% kamaytiradi. yaxlitlash xatoliklari esa aniq usullar yordamida yechganga qaraganda kamroq ta’sir qiladi, bundan tashqari hisoblash vaqtidagi xatoliklar yechimni topishning keyingi qadamida tuzatiladi. algebraik tenglamalar sistemasini takribiy yechishning keng tarqalgan usullaridan biri zeydel usulidan iboratdir. usulning mazmuni: faraz kiliylik (3.1) sistema berilgan bo’lsin va undagi diogonal koeffisentlar noldan farqli bo’lsin, ya’ni . sistemaning birinchi tenglamasini ga, ikkinchisini ga nisbatan yechib quyidagi sistemaga ega bo’lamiz. , (3.2) ……………………………… . bu yerda , da va , da. (3.2) sistemani ketma-ket yakinlashish usulida …

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i yaqinlashuvchi bo’ladi, agarda tengsizlik bajarilsa, ya’ni har bir tenglamada diogonal koeffisiyentlarning moduli qolgan boshqa koeffisiyentlar modullarining yig’indisidan katta bo’lsa( ozod hadlarni hisobga olmaganda). misol. zeydel usulini qo’llab quyidagi sistemaning yechimini topaylik: ; ; (3.4) . yechish: berilgan sistemani (3.2) ko’rinishdagi sistemaga keltiramiz: ; ; . haqiqitan ham bu sistema uchun zaruriy shart bajariladi: nolinchi yakinlashish sifatida u holda zeydel usulining keyingi yaqinlashishi quyidagicha bo’ladi: ; ; ; k=2 bo’lganda ; ; ; jadval 3.1 (3.4) sistema noma’lumlarining qiymatlari quyidagi jadvalda keltirilgan: k 0 1,2000 1,3000 1,4000 1 0,9300 0,9740 1,0192 2 1,0006 0,9979 1,0002 3 1,0001 0,9999 0,9999 4 1,0000 1,0000 0,9999 5 1,0000 1,0000 1,0000 6 1,0000 1,0000 1,0000 bu yerda sistemaning haqiqiy yechimi quyidagichadir: чизиқли тенгламалар системаси 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 11. 12. 13. 14. 15. 16. 17. 18. 19. 20 21. 22. 23. 24. 25. 26. 27. 28. 29. 30 …

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$likkacha davom ettiramiz. ushbu misolda berilgan tenglamalar sistemasi 1 ta haqiqiy yechimga ega ekanligini quyidagi maple dastur va grafiklardan ko’rish mumkin: > plots[implicitplot]({2*x^3-y^2-1=0,x*y^3-y-4=0},x=-2..2,y=-3..3); solve({2*x^3-y^2-1=0,x*y^3-y-4=0},{x,y}); allvalues(%); evalf(%); oddiy iterasiya usuli. (1) sistemani (3) ko’rinishda yozib olamiz. funkiyalar iterasiyalovchi funksiyalar deb yuritiladi. taqribiy yechimni topish algoritmi (4) ko’rinishda beriladi. bu yerda - birinchi yaqinlashish qiymatlari. (4) iterasion hisoblash jarayoni yaqinlashuvchi bo’ladi, agarda (5) tengsizliklar bajarilsa. misol. quyidagi sistemaning yechimini oddiy iterasiya usulida 0,001 aniqlikda taqribiy hisoblang. yechish. iterasiya usulini qo’llash uchun berilgan sistemani ko’rinishda yozib olamiz. kvadrat sohani qaraylik. agar shu sohaga qarashli bo’lsa, u holda o’rinli bo’ladi. demak shu sohadan ixtiyoriy tanlaganimizda ham ham o’sha sohaga tegishli bo’ladi. bundan esa (5) yaqinlashish shartining bajarilishi kelib chiqadi, ya’ni o’rinli bo’ladi. demak, qaralayotgan kvadrat sohada yagona yechim mavjud va uni iterasiya usuli yordamida taqribiy hisoblash mumkin. dastlabki yaqinlashishni deb olaylik. hisoblashlarni shu singari davom ettirib bo’lishini aniqlaymiz. bo’lganligidan va uchinchi va to’rtinchi taqribiy …$

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kda hisoblang. № 1 № 2 № 3 № 4 № 5 № 6 № 7 № 8 № 9 № 10 № 11 № 12 № 13 № 14 № 15 № 16 № 17 № 18 № 19 № 20 № 21 № 22 № 23 № 24 № 25 № 26 oleobject3.bin oleobject50.bin image47.wmf oleobject51.bin image48.wmf oleobject52.bin image49.wmf oleobject53.bin image50.wmf oleobject54.bin image51.wmf image4.wmf oleobject55.bin image52.wmf oleobject56.bin image53.wmf oleobject57.bin image54.wmf oleobject58.bin image55.wmf oleobject59.bin image56.wmf oleobject4.bin oleobject60.bin image57.wmf oleobject61.bin image58.wmf oleobject62.bin image59.wmf oleobject63.bin image60.wmf oleobject64.bin image61.wmf image5.wmf oleobject65.bin image62.wmf oleobject66.bin image63.wmf oleobject67.bin image64.wmf oleobject68.bin image65.wmf oleobject69.bin image66.wmf oleobject5.bin oleobject70.bin image67.wmf oleobject71.bin image68.wmf oleobject72.bin image69.wmf oleobject73.bin image70.wmf oleobject74.bin image71.wmf image6.wmf oleobject75.bin image72.wmf oleobject76.bin image73.wmf oleobject77.bin image74.wmf oleobject78.bin image75.wmf oleobject79.bin image76.wmf oleobject6.bin oleobject80.bin image77.wmf oleobject81.bin image78.wmf oleobject82.bin image79.wmf oleobject83.bin image80.wmf oleobject84.bin image81.wmf image7.wmf oleobject85.bin image82.wmf oleobject86.bin image83.wmf oleobject87.bin image84.png image85.wmf image86.wmf oleobject88.bin image87.wmf oleobject7.bin oleobject89.bin image88.wmf oleobject90.bin oleobject91.bin image89.wmf oleobject92.bin image90.wmf …

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image108.wmf oleobject109.bin image109.wmf oleobject110.bin image110.wmf oleobject111.bin image111.wmf oleobject112.bin image112.wmf oleobject113.bin image10.wmf image113.wmf oleobject114.bin image114.wmf oleobject115.bin image115.wmf oleobject116.bin image116.wmf oleobject117.bin image117.wmf oleobject118.bin oleobject10.bin image118.wmf oleobject119.bin image119.wmf oleobject120.bin image120.wmf oleobject121.bin image121.wmf oleobject122.bin image122.wmf oleobject123.bin image11.wmf image123.wmf oleobject124.bin image124.wmf oleobject125.bin image125.wmf oleobject126.bin image126.wmf oleobject127.bin image127.wmf oleobject128.bin oleobject11.bin image128.wmf oleobject129.bin image129.wmf oleobject130.bin image130.wmf oleobject131.bin image131.wmf oleobject132.bin image12.wmf oleobject12.bin image13.wmf oleobject13.bin image14.wmf oleobject14.bin image15.wmf oleobject15.bin image16.wmf oleobject16.bin oleobject17.bin image17.wmf oleobject18.bin image18.wmf oleobject19.bin image19.wmf oleobject20.bin image20.wmf oleobject21.bin image21.wmf oleobject22.bin image22.wmf oleobject23.bin image1.wmf oleobject24.bin oleobject25.bin image23.wmf oleobject26.bin oleobject27.bin image24.wmf oleobject28.bin image25.wmf oleobject29.bin image26.wmf oleobject1.bin oleobject30.bin image27.wmf oleobject31.bin image28.wmf oleobject32.bin image29.wmf oleobject33.bin image30.wmf oleobject34.bin image31.wmf image2.wmf oleobject35.bin image32.wmf oleobject36.bin image33.wmf oleobject37.bin image34.wmf oleobject38.bin image35.wmf oleobject39.bin image36.wmf oleobject2.bin oleobject40.bin image37.wmf oleobject41.bin image38.wmf oleobject42.bin image39.wmf oleobject43.bin image40.wmf oleobject44.bin image41.wmf image3.wmf oleobject45.bin image42.wmf oleobject46.bin image43.wmf oleobject47.bin image44.wmf oleobject48.bin image45.wmf oleobject49.bin image46.wmf ï î ï í ì = + + - = + - = + + - 7 8 2 15 …

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chiziqli algebraik tenglamalar sistamasini (chats) yechishning taqribiy usullari. zeydel usuli zeydel usuli faraz qilaylik quyidagi sistema berilgan bo’lsin: , , (3.1) ……………………….. . takribiy yechish usullari orqali sistemaning yechimini aniqlaymiz (ya’ni shunday usullarni qo’llash lozimki hisoblashlarni yaxlitlanmasdan yechim ni ma’lum bir aniqlikda topish lozim). agar (3.1) ning noma’lumlari soni ko’p bo’lsa, uning aniq yechimini topish qiyinlashadi. bunday hollarda sistemaning yechimlarini topish uchun taqribiy usullardan foydalaniladi. bu esa yechimni topish vaqtini 20-30% kamaytiradi. yaxlitlash xatoliklari esa aniq usullar yordamida yechganga qaraganda kamroq ta’sir qiladi, bundan tashqari hisoblash vaqtidagi xatoliklar yechimni topishning keyingi qadamida tuzatiladi. algebraik tengla...

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