Kinds of Problems, Algorithms, and Parallelism

• Problems

  • Linear Systems: Ax = b
  • Least Squares: minx||Ax - b||2
  • Eigenvalue problems: Ax = ?x
    

• Algorithms

  • Direct
    • “Solution” after fixed number of steps
    • Manipulate matrix entries directly

• Algorithms

  • Iterative
    • Error decreases after each step
    • Stop iteration after error small enough
    • Often access matrix A only via routine
      • y = Ax or y = ATx

• Parallelism

  • Distributed memory
  • Shared memory with threads
  • Interested in scalibility
    • 10’s, 100’s, 1000’s procs

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