x = A b; in Matlab

x = A b;

  1. Is A square?
    no => use QR to solve least squares problem.
  2. Is A triangular or permuted triangular?
    yes => sparse triangular solve
  3. Is A symmetric with positive diagonal elements?
    yes => attempt Cholesky after symmetric minimum degree.
  4. Otherwise
    => use LU on A (:, colamd(A))

finnix

Finnix is a self-contained, bootable Linux CD distribution (“LiveCD”) for system administrators, based on Debian. You can mount and manipulate hard drives and partitions, monitor networks, rebuild boot records, install other operating systems, and much more. Finnix includes the latest technology for system administrators, with Linux kernel 3.0, x86 and PowerPC support, hundreds of sysadmin-geared packages, and much more. And above all, Finnix is small; currently the entire distribution is over 400MiB, but is dynamically compressed into a small bootable image. Finnix is not intended for the average desktop user, and does not include any desktops, productivity tools, or sound support, in order to keep distribution size low.

x = A \ b; in Matlab

x = A \ b;

  1. Is A square?
    no => use QR to solve least squares problem.
  2. Is A triangular or permuted triangular?
    yes => sparse triangular solve
  3. Is A symmetric with positive diagonal elements?
    yes => attempt Cholesky after symmetric minimum degree.
  4. Otherwise
    => use LU on A (:, colamd(A))

x = A b; in Matlab

x = A b;

  1. Is A square?
    no => use QR to solve least squares problem.
  2. Is A triangular or permuted triangular?
    yes => sparse triangular solve
  3. Is A symmetric with positive diagonal elements?
    yes => attempt Cholesky after symmetric minimum degree.
  4. Otherwise
    => use LU on A (:, colamd(A))