Numerical Constraints

• Numerical methods also have problems when:

  • Equations are degenerate "within round-off error".
  • Accumulated round-off errors swamp solution (magnitude of a's and x's varies wildly).

• For n,m < 50, single precision usually OK.

• For n,m < 200, double precision usually OK.

• For 200 < n,m < few thousand, solutions possible only for sparse systems (lots of a's zero).

Notes: