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Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Gauss Iteration Example** - **Example:** Solve the equation \( x - \sqrt{x} - 1 = 0 \). - Assume \( x^{(v+1)} = 1 + \sqrt{x^{(v)}} \). **Procedure:** - Let \( k = 0 \) and arbitrarily guess \( x^{(0)} = 1 \) to begin solving. **Iteration Table:** | Iteration \( k \) | \( x^{(v)} \) | |-------------------|---------------| | 0 | 1 | | 1 | 2 | | 2 | 2.41421 | | 3 | 2.55538 | | 4 | 2.59805 | | 5 | 2.61185 | | 6 | 2.61612 | | 7 | 2.61744 | | 8 | 2.61785 | | 9 | ? | **Explanation:** - This example demonstrates the iterative process for solving the given equation using the Gauss Iteration method. The table shows the progression of values through iterative calculation, converging towards a solution. Each row represents an iteration where \( x^{(v)} \) is updated based on the previous value.
Transcribed Image Text:**Gauss Iteration Example** - **Example:** Solve the equation \( x - \sqrt{x} - 1 = 0 \). - Assume \( x^{(v+1)} = 1 + \sqrt{x^{(v)}} \). **Procedure:** - Let \( k = 0 \) and arbitrarily guess \( x^{(0)} = 1 \) to begin solving. **Iteration Table:** | Iteration \( k \) | \( x^{(v)} \) | |-------------------|---------------| | 0 | 1 | | 1 | 2 | | 2 | 2.41421 | | 3 | 2.55538 | | 4 | 2.59805 | | 5 | 2.61185 | | 6 | 2.61612 | | 7 | 2.61744 | | 8 | 2.61785 | | 9 | ? | **Explanation:** - This example demonstrates the iterative process for solving the given equation using the Gauss Iteration method. The table shows the progression of values through iterative calculation, converging towards a solution. Each row represents an iteration where \( x^{(v)} \) is updated based on the previous value.
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