SuiteSparseQR swMATH ID: 7348 Software Authors: Timothy A. Davis Description: 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. Homepage: http://dl.acm.org/citation.cfm?id=2049670 Related Software: SuitSparseQR; SparseMatrix; LSQR; Matlab; CHOLMOD; LAPACK; MIQR; CSparse; LSMR; SuiteSparse; UMFPACK; HSL; COLAMD; qr_mumps; Scotch; MUMPS; Regularization tools; MatrixMarket; Gmsh; METIS Cited in: 42 Publications all top 5 Cited by 91 Authors 4 Nürnberg, Robert 3 Batselier, Kim 3 Buttari, Alfredo 3 Davis, Timothy Alden 3 De Moor, Bart L. R. 3 Dreesen, Philippe 3 Scott, Jennifer A. 2 Barrett, John William 2 Garcke, Harald 2 Hanke, Michael 2 März, Roswitha 1 Agnese, Marco 1 Agullo, Emmanuel 1 Akbarzadeh, Siamak 1 Arioli, Mario 1 Aykanat, Cevdet 1 Bedrossian, Jacob 1 Brenner, Holger 1 Brust, Johannes J. 1 Bujanović, Zvonimir 1 Carlebach, Eyal 1 Cayrols, Sebastien 1 Chandrasekaran, Shivkumar 1 Chen, Qiao 1 Daas, Hussam Al 1 Darve, Eric 1 De Goes, Fernando 1 De Lathauwer, Lieven 1 Demmel, James Weldon 1 Desbrun, Mathieu 1 Druinsky, Alex 1 Duff, Iain S. 1 Essid, Montacer 1 Everdij, Frank P. X. 1 Foster, Leslie V. 1 Gallopoulos, Efstratios 1 Girolami, Mark A. 1 Gnanasekaran, Abeynaya 1 Gould, Nicholas Ian Mark 1 Grigori, Laura 1 Guermouche, Abdou 1 Hauberg, Søren 1 Hayami, Ken 1 Jiao, Xiangmin 1 Jolivet, Pierre 1 Jones, Daniel C. 1 Kodsi, Costy 1 Kressner, Daniel 1 Lasanen, Sari 1 Lei, Yuan 1 Lloberas-Valls, Oriol 1 Lopez, Florent 1 Lundquist, Tomas 1 Luskin, Mitchell 1 Maier, Matthias Sebastian 1 Malan, Arnaud George 1 Manguoglu, Murat 1 Marcia, Roummel F. 1 Margetis, Dionisios 1 Markkanen, Markku 1 Memari, Pooran 1 Mhaskar, Hrushikesh N. 1 Morikuni, Keiichi 1 Mullen, Patrick 1 Müller, Jens-Dominik 1 Nordström, Jan 1 Petra, Cosmin G. 1 Ploskas, Nikolaos 1 Ranka, Sanjay 1 Rixen, Daniel J. 1 Roininen, Lassi 1 Sacconi, Andrea 1 Sahinidis, Nikolaos V. 1 Samaras, Nikolaos 1 Saunders, Michael A. 1 Sid-Lakhdar, Wissam M. 1 Sifakis, Eftychios 1 Simone, Angelo 1 Sluys, Lambertus Johannes 1 Sobczyk, Aleksandros 1 Solomon, Justin 1 Steinbuch, Jonathan 1 Teran, Joseph M. 1 Toledo, Sivan 1 Torun, F. Sukru 1 Vanderstukken, Jeroen 1 von Brecht, James H. 1 Wang, Yang 1 Yeralan, Sencer Nuri 1 Zhang, Xingchen 1 Zhu, Siwei all top 5 Cited in 18 Serials 8 SIAM Journal on Scientific Computing 6 ACM Transactions on Mathematical Software 6 SIAM Journal on Matrix Analysis and Applications 4 Journal of Computational Physics 4 Numerical Algorithms 1 Journal of Computational and Applied Mathematics 1 Numerische Mathematik 1 Applied Numerical Mathematics 1 ACM Transactions on Graphics 1 International Journal of Algebra and Computation 1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 1 Linear Algebra and its Applications 1 Numerical Linear Algebra with Applications 1 International Journal of Computational Fluid Dynamics 1 International Journal of Numerical Analysis and Modeling 1 Inverse Problems and Imaging 1 Mathematical Programming Computation 1 Berichte aus der Mathematik all top 5 Cited in 16 Fields 37 Numerical analysis (65-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Computer science (68-XX) 3 Partial differential equations (35-XX) 3 Statistics (62-XX) 3 Operations research, mathematical programming (90-XX) 2 Combinatorics (05-XX) 2 Commutative algebra (13-XX) 2 Ordinary differential equations (34-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 1 Algebraic geometry (14-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year