SuiteSparseQR swMATH ID: 7348 Software Authors: Davis, Timothy A. 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; Matlab; LAPACK; CSparse; LSQR; MIQR; UMFPACK; CHOLMOD; COLAMD; LSMR; SuiteSparse; CRAIG; HSL; Regularization tools; Algorithm 980; CIMGS; HSL_MI28; CUTEst; mctoolbox Cited in: 53 Documents all top 5 Cited by 114 Authors 5 Scott, Jennifer 4 Davis, Timothy Alden 4 Nürnberg, Robert 3 Batselier, Kim 3 Buttari, Alfredo 3 De Moor, Bart L. R. 3 Dreesen, Philippe 2 Barrett, John William 2 Garcke, Harald 2 Hanke, Michael 2 Lourenco, Christopher J. 2 März, Roswitha 2 Moreno-Centeno, Erick 2 Tůma, Miroslav 1 Agnese, Marco 1 Agullo, Emmanuel 1 Akbarzadeh, Siamak 1 Alvarruiz, Fernando 1 Arioli, Mario 1 Aykanat, Cevdet 1 Bedrossian, Jacob 1 Bijnens, Johan 1 Brenner, Holger 1 Brust, Johannes J. 1 Bujanović, Zvonimir 1 Campos, Carmen 1 Carlebach, Eyal 1 Cayrols, Sebastien 1 Chandrasekaran, Shivkumar 1 Chen, Jinhao 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 Fabiani, Gianluca 1 Foster, Leslie V. 1 Galaris, Evangelos 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 Hong, Li-Dan 1 Howell, Jason S. 1 Jiao, Xiangmin 1 Jolivet, Pierre 1 Kodsi, Costy 1 Kressner, Daniel 1 Ku, Cheng-Yu 1 Lasanen, Sari 1 Lei, Wanzhou 1 Lei, Yuan 1 Liu, Chih-Yu 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 Nurbekyan, Levon 1 Pawlak, Tomasz P. 1 Petra, Cosmin G. 1 Ploskas, Nikolaos 1 Ranka, Sanjay 1 Rixen, Daniel J. 1 Roininen, Lassi 1 Román, Jose E. 1 Ruiz-Vidal, Joan 1 Russo, Lucia 1 Sacconi, Andrea 1 Sahinidis, Nikolaos V. 1 Samaras, Nikolaos 1 Saunders, Michael A. 1 Sid-Lakhdar, Wissam M. 1 Siettos, Constantinos I. 1 Sifakis, Eftychios 1 Simone, Angelo 1 Sluys, Lambertus Johannes 1 Sobczyk, Aleksandros 1 Solomon, Justin ...and 14 more Authors all top 5 Cited in 24 Serials 9 SIAM Journal on Scientific Computing 8 ACM Transactions on Mathematical Software 6 SIAM Journal on Matrix Analysis and Applications 4 Journal of Computational Physics 4 Numerical Algorithms 2 Journal of Computational and Applied Mathematics 2 Numerical Linear Algebra with Applications 1 International Journal of Engineering Science 1 BIT 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 Engineering Analysis with Boundary Elements 1 International Journal of Computational Fluid Dynamics 1 Chaos 1 Journal of High Energy Physics 1 International Journal of Numerical Analysis and Modeling 1 Optimization Letters 1 Inverse Problems and Imaging 1 Mathematical Programming Computation 1 Berichte aus der Mathematik all top 5 Cited in 20 Fields 46 Numerical analysis (65-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 6 Operations research, mathematical programming (90-XX) 4 Partial differential equations (35-XX) 4 Mechanics of deformable solids (74-XX) 3 Commutative algebra (13-XX) 3 Statistics (62-XX) 3 Computer science (68-XX) 3 Fluid mechanics (76-XX) 2 Combinatorics (05-XX) 2 Ordinary differential equations (34-XX) 2 Probability theory and stochastic processes (60-XX) 2 Optics, electromagnetic theory (78-XX) 2 Biology and other natural sciences (92-XX) 1 Algebraic geometry (14-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year