Metadata
Mathematics Graduate Analyze Medium
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Metadata

  • Subject

    Mathematics

  • Education level

    Graduate

  • Cognitive goals

    Analyze

  • Difficulty estimate

    Medium

  • Tags

    Krylov, Conjugate Gradient, GMRES, preconditioning, sparse linear systems, 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

    Test students' ability to analyze convergence behavior of Conjugate Gradient and GMRES for large sparse linear systems (SPD and nonsymmetric), including effects of eigenvalue distribution and condition number, finite-precision breakdowns, restart strategies, and residual/norm histories; evaluate and compare common preconditioners (Jacobi, incomplete Cholesky/ILU, SSOR, AMG), estimate iteration counts, justify preconditioner choice, and provide concise derivations and practical tuning/implementation recommendations based on diagnostics.
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Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.