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 26 articles )
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Sorted by year (- Essid, Montacer; Solomon, Justin: Quadratically regularized optimal transport on graphs (2018)
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- Scott, Jennifer: On using Cholesky-based factorizations and regularization for solving rank-deficient sparse linear least-squares problems (2017)
- Sencer Nuri Yeralan; Timothy A. Davis; Wissam M. Sid-Lakhdar; Sanjay Ranka: Algorithm 980: Sparse QR Factorization on the GPU (2017)
- Torun, F. Sukru; Manguoglu, Murat; Aykanat, Cevdet: Parallel minimum norm solution of sparse block diagonal column overlapped underdetermined systems (2017)
- Agullo, Emmanuel; Buttari, Alfredo; Guermouche, Abdou; Lopez, Florent: Implementing multifrontal sparse solvers for multicore architectures with sequential task flow runtime systems (2016)
- Bujanović, Zvonimir; Kressner, Daniel: A block algorithm for computing antitriangular factorizations of symmetric matrices (2016)
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- Chandrasekaran, S.; Mhaskar, H. N.: A minimum Sobolev norm technique for the numerical discretization of PDEs (2015)
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- Goes, Fernando de; Memari, Pooran; Mullen, Patrick; Desbrun, Mathieu: Weighted triangulations for geometry processing (2014)
- Batselier, Kim; Dreesen, Philippe; de Moor, Bart: The geometry of multivariate polynomial division and elimination (2013)
- Batselier, Kim; Dreesen, Philippe; De Moor, Bart: A geometrical approach to finding multivariate approximate LCMs and GCDs (2013)
- Buttari, Alfredo: Fine-grained multithreading for the multifrontal $QR$ factorization of sparse matrices (2013)