>> Do algorithm authors really implement two code paths? I do sometimes. Sometimes I test the result, and if it is not correct, then I use a slower, more nume

>> Do algorithm authors really implement two code paths? I do sometimes. Sometimes I test the result, and if it is not correct, then I use a slower, more numerically stable algorithm. I'm not sure if I have ever written code that repeats the same code with quad precision, but of course that would often work. Sometimes you can compute a correction from the "residual". >>One that uses a cost function iterative algorithm to solve the matrix (this is what everybody does), and a second algorithm using the brute force approach the author showed (known not to work). We do often use Jacobi or Gauss-Seidel, or something similar (esp for computing estimates of A^(-1)b ). In those cases we never revert back to QR. We do sometimes use Jacobi or GS to improve a result obtained from an ill conditioned QR, but rarely. Many years ago, I would have the code raise an exception if the result is bad so that I would get a call. When I got such a call, I would think about how to make the algorithm more stable.