An out-of-core sparse Cholesky solver. Direct methods for solving large sparse linear systems of equations are popular because of their generality and robustness. Their main weakness is that the memory they require usually increases rapidly with problem size. We discuss the design and development of the first release of a new symmetric direct solver that aims to circumvent this limitation by allowing the system matrix, intermediate data, and the matrix factors to be stored externally. The code, which is written in Fortran and called HSL_MA77, implements a multifrontal algorithm. The first release is for positive-definite systems and performs a Cholesky factorization. Special attention is paid to the use of efficient dense linear algebra kernel codes that handle the full-matrix operations on the frontal matrix and to the input/output operations. The input/output operations are performed using a separate package that provides a virtual-memory system and allows the data to be spread over many files; for very large problems these may be held on more than one device. Numerical results are presented for a collection of 30 large real-world problems, all of which were solved successfully.

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  1. Scott, Jennifer; Tůma, Miroslav: A Schur complement approach to preconditioning sparse linear least-squares problems with some dense rows (2018)
  2. Gould, Nicholas I. M.; Robinson, Daniel P.: A dual gradient-projection method for large-scale strictly convex quadratic problems (2017)
  3. Scott, Jennifer: On using Cholesky-based factorizations and regularization for solving rank-deficient sparse linear least-squares problems (2017)
  4. Sun, Yifan; Andersen, Martin S.; Vandenberghe, Lieven: Decomposition in conic optimization with partially separable structure (2014)
  5. Castellanos, J. A.; Larrazabal, G.: A Cholesky out-of-core factorization (2013)
  6. Hogg, Jonathan D.; Scott, Jennifer A.: Pivoting strategies for tough sparse indefinite systems (2013)
  7. Hogg, Jonathan D.; Scott, Jennifer A.: An efficient analyse phase for element problems. (2013)
  8. Hogg, Jonathan; Scott, Jennifer: New parallel sparse direct solvers for multicore architectures (2013)
  9. Lu, Zheng; Tai, Yu-Wing; Deng, Fanbo; Ben-Ezra, Moshe; Brown, Michael S.: A 3D imaging framework based on high-resolution photometric-stereo and low-resolution depth (2013) ioport
  10. Agullo, Emmanuel; Guermouche, Abdou; L’Excellent, Jean-Yves: Reducing the I/O volume in sparse out-of-core multifrontal methods (2010)
  11. Amestoy, P.; Duff, I. S.; Guermouche, A.; Slavova, Tz.: Analysis of the solution phase of a parallel multifrontal approach (2010)
  12. Gould, Nicholas I. M.; Robinson, Daniel P.; Thorne, H. Sue: On solving trust-region and other regularised subproblems in optimization (2010)
  13. Hogg, J. D.; Reid, J. K.; Scott, J. A.: Design of a multicore sparse Cholesky factorization using DAGs (2010)
  14. Reid, J. K.; Scott, J. A.: An efficient out-of-core multifrontal solver for large-scale unsymmetric element problems (2009)
  15. Reid, John K.; Scott, Jennifer A.: An out-of-core sparse Cholesky solver (2009)