LU decomposition of matrices with augmented dense constraints

Sparse matrices composed of a central band and augmented dense rows and columns are becoming prevalent in the numerical solution of a large class of boundary and initial‐value problems. A Fortran Subroutine ARROW is presented for the LU decomposition and solution of linear equation systems with such a structure. The computational speed of the program is compared in MFLOPS (millions of floating point operations per second) to the LINPACK benchmark for the solution of a dense linear system and is found to be of comparable speed on both supercomputers and minicomputers. Use of the Basic Linear Algebra Subroutines (BLAS) available on most machines significantly enhances the speed of ARROW .