Thanks. I always forget about that book since I don’t have a print copy. I should probably start a new table for symmetric matrices and Cholesky factorization (LAPACK has multiple versions of those) anyways.
There is a pair of banded Cholesky routines CHOBNDN / VRBNDN in the book: Schwarz, H. R. (1991). FORTRAN-Programme zur Methode der finiten Elemente (Vol. 3). BG Teubner.
For the banded QR decomposition, I’m aware of
- routines used internally in MINPACK
- the work of Remon et. al, LAPACK-Style Codes for the QR Factorization of
Banded Matrices (PDF, 498 KB); the source code is available from Burkardt: band_qr
I’ve found a pentadiagonal LU factorization (without gaps or pivoting) in the work of C. J. Fletcher: Computational Galerkin Methods | SpringerLink (useful for 1-d quadratic FEM or for a quintic spline interpolation).
Not to forget the classic libraries: NSWC, HSL, IMSL, NAG, or even the numerical library of Moscow State University.