SuiteSparseQR
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading Building Blocks library. The symbolic analysis and ordering phase pre-eliminates singletons by permuting the input matrix A into the form [R11 R12; 0 A22] where R11 is upper triangular with diagonal entries above a given tolerance. Next, the fill-reducing ordering, column elimination tree, and frontal matrix structures are found without requiring the formation of the pattern of ATA. Approximate rank-detection is performed within each frontal matrix using Heath’s method. While Heath’s method is not always exact, it has the advantage of not requiring column pivoting and thus does not interfere with the fill-reducing ordering. For sufficiently large problems, the resulting sparse QR factorization obtains a substantial fraction of the theoretical peak performance of a multicore computer.
This software is also peer reviewed by journal TOMS.
This software is also peer reviewed by journal TOMS.
Keywords for this software
References in zbMATH (referenced in 14 articles )
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Sorted by year (- Bujanović, Zvonimir; Kressner, Daniel: A block algorithm for computing antitriangular factorizations of symmetric matrices (2016)
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- Buttari, Alfredo: Fine-grained multithreading for the multifrontal $QR$ factorization of sparse matrices (2013)
- Foster, Leslie V.; Davis, Timothy A.: Algorithm 933, reliable calculation of numerical rank, null space bases, pseudoinverse solutions, and basic solutions using SuiteSparseQR (2013)
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- Barrett, John W.; Garcke, Harald; Nürnberg, Robert: Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves (2012)
- Barrett, John W.; Garcke, Harald; Nürnberg, Robert: Elastic flow with junctions: variational approximation and applications to nonlinear splines (2012)