This module solves a system of linear equations whose matrix is banded, symmetric and positive deﬁnite. It uses block Cholesky factorization, taking advantage of any variation in bandwidth. It has an option for storing the matrix itself as well as its factorization. A secondary entry provides for further systems with the same matrix but diﬀerent right-hand sides to be solved economically. The secondary entry can also be used to calculate residuals, needed for iterative reﬁnement, provided the matrix itself has been stored. For very large systems or if restart facilities are desired, HSL_MA55 uses a direct-access ﬁle for the factors and a sequential ﬁle for the matrix.
The user must ﬁrst specify all the row lengths. The matrix itself is supplied by blocks of rows using reverse communication. The blocking for input is chosen by the user and is independent of the blocking used for solution.
MC60 may be used to get a good ordering.