1. Introduction This work was started by Gustavson and Toledo described in [8, 16].
These papers describe the application of recursion to the numerical dense
linear algebra algorithms. Recursion leads to automatic variable blocking
for the dense linear-algebra algorithms. This leads to modifications of the
LAPACK [2] algorithms. LAPACK's level-2 version routines are trans-
formed into level-3 codes by using recursion.
Fortran 90 allows recursion (see [15]). The programs are very concise
and the recursion part is automatic as it is handled by the compiler. The
intermediate subroutines obey the Fortran 90 standard too (see [5]).
Section 2 shows the recursive Cholesky factorization algorithm. Section
3 formulates the recursive algorithm of Gaussian elimination without pivot-
ing and LU factorization with partial pivoting. Section 4 explains two recur-
sive BLAS: RTRSM and RSYRK. Section 5 demonstrates the factorization
algorithm using the pivoting strategy introduced by Bunch-Kaufman for
symmetric indefinite matrices (see [6, pp. 161–170]).
