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Are you guys able to offer any guidance on numerical stability of linear algebra problems? For example, the Woodbury matrix identity's stability seems uncertain

by meisel 3y ago

Are you guys able to offer any guidance on numerical stability of linear algebra problems? For example, the Woodbury matrix identity's stability seems uncertain based on https://mathoverflow.net/questions/80340/special-considerations-when-using-the-woodbury-matrix-identity-numerically https://mathoverflow.net/questions/80340/special-considerati...

bee_rider 3y ago
I think it depends on the nature of the matrices; it doesn’t make sense to use if your A matrix is just some general dense matrix for example.
- meisel 3y ago
  Why doesn't it make sense to use in that case?
  - bee_rider 3y ago
    The dimensions of (A-UBU’) are the same as the dimensions of A. After you apply Woodbury, you have inv(A) - (other stuff) So, it only makes sense if A is much easier to solve than (A-UBU’).