Metadata
Mathematics Undergraduate Analyze Medium
Metadata
  • Subject

    Mathematics

  • Education level

    Undergraduate

  • Cognitive goals

    Analyze

  • Difficulty estimate

    Medium

  • Tags

    iterative methods, Jacobi, Gauss–Seidel, SOR, spectral radius, convergence

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • 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.
Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.