Skip to main content
MathOverflow

Return to Answer

added 113 characters in body
Source Link
Federico Poloni
Federico Poloni
  • 20.2k
  • 2
  • 82
  • 120

This subject has been studied in literature --- it turns out that for some class of matrices (such as M-matrices) you can obtain componentwise accurate solutions. A good starting point is the section on "accurate floating point computation" on Jim Demmel's home page; other good search terms are "accurate linear algebra" and "componentwise error analysis". Recent literature has focused more on accurate eigenvalue computation rather than linear systems, but there are results also for them.

EDIT: And let me add that discretizing $\Delta$ with the usual finite-difference scheme results in an M-matrix.

This subject has been studied in literature --- it turns out that for some class of matrices (such as M-matrices) you can obtain componentwise accurate solutions. A good starting point is the section on "accurate floating point computation" on Jim Demmel's home page; other good search terms are "accurate linear algebra" and "componentwise error analysis". Recent literature has focused more on accurate eigenvalue computation rather than linear systems, but there are results also for them.

This subject has been studied in literature --- it turns out that for some class of matrices (such as M-matrices) you can obtain componentwise accurate solutions. A good starting point is the section on "accurate floating point computation" on Jim Demmel's home page; other good search terms are "accurate linear algebra" and "componentwise error analysis". Recent literature has focused more on accurate eigenvalue computation rather than linear systems, but there are results also for them.

EDIT: And let me add that discretizing $\Delta$ with the usual finite-difference scheme results in an M-matrix.

Source Link
Federico Poloni
Federico Poloni
  • 20.2k
  • 2
  • 82
  • 120

This subject has been studied in literature --- it turns out that for some class of matrices (such as M-matrices) you can obtain componentwise accurate solutions. A good starting point is the section on "accurate floating point computation" on Jim Demmel's home page; other good search terms are "accurate linear algebra" and "componentwise error analysis". Recent literature has focused more on accurate eigenvalue computation rather than linear systems, but there are results also for them.