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Abstract
Ushbu maqolada chiziqli tenglamalar sistemalarini yechishning zamonaviy raqamli usullari tahlil qilinadi. Asosiy e’tibor to‘g‘ridan-to‘g‘ri metodlar (Gauss, Gauss-Jordan) va iteratsion metodlar (Jacobi, Gauss-Seidel, relaxatsiya metodlari)ning samaradorligi va aniqligiga qaratilgan. Tadqiqotda turli usullar yordamida sistemalarning yechimlari hisoblandi, xatoliklar va hisoblash samaradorligi solishtirildi. Natijalar chiziqli tenglamalar sistemalarini yechishda metod tanlash va hisoblash samaradorligini oshirish bo‘yicha amaliy tavsiyalar beradi. Ushbu maqola matematika, muhandislik hisoblashlari va ilmiy tadqiqotlarda chiziqli tenglamalar sistemalarini samarali yechish imkoniyatlarini ko‘rsatadi.
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