Algorithm 664: A Gauss algorithm to solve systems with large, banded matrices using random-access disk storage

ABSTRACT

A FORTRAN 77 implementation of a Gauss algorithm with partial pivoting for banded matrices is described. The algorithm keeps only part of the matrix that is necessary for the actual computation in memory. This allows large systems to be solved on machine without virtual memory, or if the virtual memory is too small for the problem.

REFERENCES

• 1: DONGARRA, J. J., MOLER, C. B., BUNCH, J. R., AND STEWART, G.W. LINPACK User's Guide. SIAM, Philadelphia, Penn., 1979.
• 2: ISAACSON, E., AND KELLER, H. B. Analysis of Numerical Methods. John Wiley, New York, 1966.
• 3: KELLER, H. S. Numerical solution of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory, P. Rabinowitz (Ed.). Academic Press, New York, 1977.
• 4: SCHRAUF, G. The first instability in Taylor-Couette flow. J. Fluid Mech. 166 (May 1986), 287-3O3.
• 5: SCHRAUF, G., AND KRAUSE, E. Symmetric and asymmetric Taylor vortices in a spherical gap. In Laminar-Turbulent Transition IUTAM Symposium Novosibirsk, 1984, V. V. Kozlov (Ed.). Springer-Verlag, Berlin, 1985.

INDEX TERMS

Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms
      G.1.3 Numerical Linear Algebra
          Subjects: Sparse, structured, and very large systems (direct and iterative methods); Linear systems (direct and iterative methods)

General Terms:
Algorithms

Keywords:
Gauss algorithm, banded matrices