Question
निम्नलिखित समीकरण निकाय को हल करने के लिए गाउस–सीडल पुनरावृत्ति विधि को आव्यूह रूप में स्थापित कीजिए :
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दिखाइए कि पुनरावृत्ति विधि अभिसरित होती है और अतः इसकी अभिसरण दर ज्ञात कीजिए। (5)
Answer :
Word Count : 318
समीकरण निकाय है: [ \begin{bmatrix} 1 & 1 & 1 \ 4 & 3 & -1 \ 3 & 5 & 3 \end{bmatrix} \begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 1 \ 6 \ 4 \end{bmatrix}. ] गाउस–सीडल विधि के लिए पहले इसे पुनरावृत्ति रूप में लिखते हैं। समीकरणों को (x, y, z) के लिए अलग करते हैं: 1. (x + y + z = 1 \implies x = 1 - y - z) 2. (4x + _________ _____ ___ _________ ___ _____ __________ ______ ______ _______.
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समीकरण निकाय है: [ \begin{bmatrix} 1 & 1 & 1 \ 4 & 3 & -1 \ 3 & 5 & 3 \end{bmatrix} \begin{bmatrix} x \ y \ z \end{bmatrix} = \begin{bmatrix} 1 \ 6 \ 4 \end{bmatrix}. ] गाउस–सीडल विधि के लिए पहले इसे पुनरावृत्ति रूप में लिखते हैं। समीकरणों को (x, y, z) के लिए अलग करते हैं: 1. (x + y + z = 1 \implies x = 1 - y - z) 2. (4x + _________ _____ ___ _________ ___ _____ __________ ______ ______ _______.
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