Metadata
Mathematics Undergraduate Analyze Medium-
Subject
Mathematics
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Education level
Undergraduate
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Cognitive goals
Analyze
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Difficulty estimate
Medium
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Tags
iterative methods, Jacobi, Gauss–Seidel, SOR, spectral radius, convergence
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Number of questions
5
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Created on
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Generation source
Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini
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License
CC0 Public domain
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Prompt
Assess students' ability to analyze convergence of stationary iterative methods for linear systems: derive iteration matrices for Jacobi, Gauss–Seidel, and SOR; state and apply the spectral radius criterion for convergence; use matrix properties (strict diagonal dominance, symmetric positive definiteness) and Gershgorin bounds to determine convergence; compute or estimate spectral radii for examples; select an optimal relaxation parameter ω for SOR and compare convergence rates with justification.
Review & Revise
Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%
Mock data used for demo purposes.