NOCHIZIQLI ALGEBRAIK TIZIMLARNI TAHLIL QILISHDA NYUTON KO‘PYOQLILARINING MINKOVSKIY YIG‘INDILARI
Qabul qilingan: 2026-05-30
Nashr etilgan: 2026-06-06
Annotatsiya
Nyuton ko‘pyoqliklarining Minkovskiy yig‘indilariga asoslangan geometrik yondashuv nochiziqli algebraik sistemalarni tahlil qilish uchun taqdim etildi. Sistema uchun umumiy Nyuton-Minkovskiy ko‘pyoqligi qurish orqali muhim yoqlarni aniqlash, ularga mos normal konuslarni topish va dastlabki sistemaning muhim lokal xossalarini saqlovchi qisqartma sistemalarni hosil qilish imkoniyati yaratildi. Motzkin–Burger algoritmidan foydalanish konus generatorlarini hisoblashni hamda lokal yechimlarni tahlil qilishni sezilarli darajada yengillashtiradi. Olingan natijalar Minkovskiy yig‘indilarining nochiziqli algebraik sistemalarning tuzilishi va lokal xatti-harakatini o‘rganishda samarali vosita ekanligini tasdiqlaydi. Kelgusidagi tadqiqotlar ushbu yondashuvni yuqori o‘lchamli sistemalarga kengaytirish hamda uni kompyuter algebra tizimlarida samarali amalga oshirishga qaratilishi mumkin.
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