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Arithmetic
- What a float can hold
- Cancellation takes the answer, not a digit
- The order they are added in
- Buying the accuracy back
- Where the hardware went
- The other half of a format
- A norm that overflows before it is a norm
- The numbers below the smallest one
Error
- The exact answer to a nearby problem
- A small residual is not a small error
- The condition number is an amplifier
- An answer that is known
Elimination
Orthogonality
Leastsquares
Spectra
- Symmetry is worth more than precision
- The best approximation there is
- Rank is a decision
- The algorithm the libraries actually run
- The form that makes it affordable
- The form a real matrix can reach
- Two shifts that are never formed
- A condition number for one eigenvalue
Iterative
- The rate the condition number predicts
- An orthogonalisation nobody calls one
- Changing the condition number on purpose
- The spectrum that predicts nothing
- A rate that is known in advance
- The error smoothing cannot reach
- The same problem on a coarser grid
- A rate that does not notice the size
Sparsity
- The factor is not sparse
- The order decides the memory
- Two ends of the same arrow
- Structure and stability stop being separable
- A threshold between fill and growth
- What the symbolic phase can only bound