Least squares solution of nearly square overdetermined sparse linear systems

The solution of nearly square overdetermined linear systems is studied. The sparse QR technique is compared with two sparse LU-based techniques. Numerical tests with real-world and artificial matrices indicate that the LU techniques are more accurate for incompatible right-hand sides. Also, the amount of floating point operations required by LU techniques is approximately one half smaller than QR for nearly square matrices. A new derivation is presented for a direct triangular factorization approach. Extensive numerical testing was done using MATLAB and is documented in the article.