CHOLMOD swMATH ID: 4412 Software Authors: Chen, Y., Davis, T.A., Hager, W.W., Rajamanickam, S Description: Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate. CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLABTM interfaces. It appears in MATLAB 7.2 as x = A when A is sparse symmetric positive definite, as well as in several other sparse matrix functions. Homepage: http://www.cise.ufl.edu/research/sparse/cholmod/ Related Software: UMFPACK; SparseMatrix; LAPACK; CSparse; Matlab; AMD; SuperLU; Eigen; PETSc; PARDISO; MA57; MUMPS; BLAS; CUTEst; SuiteSparseQR; METIS; LDL; COLAMD; NETLIB LP Test Set; ARPACK Cited in: 108 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones. Zbl 1230.90006Andersen, Martin S.; Dahl, Joachim; Vandenberghe, Lieven 2010 all top 5 Cited by 242 Authors 9 Davis, Timothy Alden 5 Madden, Niall 5 Rumpf, Martin 4 Scott, Jennifer A. 3 Boman, Erik G. 3 Boyd, Stephen Poythress 3 Calo, Victor Manuel 3 Hager, William W. 3 MacLachlan, Scott P. 3 Rojas, Sergio 3 Wirth, Benedikt 2 Andersen, Martin S. 2 Bellavia, Stefania 2 Berkels, Benjamin 2 Dahl, Joachim 2 Darve, Eric 2 De Simone, Valentina 2 di Serafino, Daniela 2 Gomes, Francisco A. M. 2 Gonzalez, Manuel 2 Hinze, Michael 2 Hogg, Jonathan D. 2 Kahle, Christian 2 Li, Ruipeng 2 Luaces, Alberto 2 Morini, Benedetta 2 Nhan, Thái Anh 2 Rajamanickam, Sivasankaran 2 Russell, Stephen J. 2 Saad, Yousef 2 Sassen, Josua 2 Senne, Thadeu A. 2 Vandenberghe, Lieven 1 Akyildiz, Ömer Deniz 1 Al Akhras, H. 1 Andersen, Hans-Erik 1 Andreassen, Erik 1 Anitescu, Mihai 1 Antonietti, Paola Francesca 1 Argyros, Antonis A. 1 Aune, Erlend 1 Bae, Daesung 1 Bakalakos, Serafeim 1 Balzer, Jonathan 1 Banerjee, Sudipto 1 Bao, Hujun 1 Bartel, Andreas 1 Bastian, Peter 1 Behnoudfar, Pouria 1 Bollhöfer, Matthias 1 Bommes, David 1 Bouillaguet, Charles 1 Cambier, Léopold 1 Carlebach, Eyal 1 Chen, Chao 1 Chow, Edmond G. W. 1 Chow, Peter 1 Cier, Roberto J. 1 Clausen, Anders 1 Clemens, Markus 1 Cook, Bruce D. 1 Crane, Keenan 1 Crouch, Jessica 1 Datta, Abhirup 1 de Dreuzy, Jean-Raynald 1 De Gersem, Herbert 1 de Hoop, Maarten V. 1 De Marchi, Alberto 1 De Ponti, Jacopo Maria 1 De Sterck, Hans 1 Delaplace, Claire 1 D’Elia, Marta 1 Demkowicz, Leszek F. 1 Desbrun, Mathieu 1 Donfack, Simplice 1 Dopico, Daniel Dopico 1 Druinsky, Alex 1 Duffin, Connor 1 Dunson, David Brian 1 Eckstein, Jonathan 1 Effland, Alexander 1 Eftekhari, Aryan 1 Eidsvik, Jo 1 Elgammal, Ahmed 1 Elguedj, Thomas 1 Erhel, Jocelyne 1 Erickson, Brittany A. 1 Erlandson, Lucas 1 Ern, Alexandre 1 Essid, Montacer 1 Falgout, Robert D. 1 Fan, Shanhui 1 Fang, Yu 1 Fialko, S. Yu. 1 Fialko, Sergiy 1 Finley, Andrew O. 1 Formaggia, Luca 1 Foster, John T. jun. 1 Fougner, Christopher 1 Franken, Martina ...and 142 more Authors all top 5 Cited in 47 Serials 15 SIAM Journal on Scientific Computing 9 Computer Methods in Applied Mechanics and Engineering 8 ACM Transactions on Mathematical Software 4 Computational Mechanics 4 SIAM Journal on Matrix Analysis and Applications 3 Journal of Computational Physics 3 ACM Transactions on Graphics 3 Computational Optimization and Applications 3 Numerical Linear Algebra with Applications 2 Computer Physics Communications 2 Computer Aided Geometric Design 2 Journal of Scientific Computing 2 Mathematical Programming. Series A. 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Electronic Transactions on Numerical Analysis 1 Advances in Computational Mathematics 1 Mathematical Problems in Engineering 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Multibody System Dynamics 1 Archives of Computational Methods in Engineering 1 Foundations of Computational Mathematics 1 Computational Methods in Applied Mathematics 1 Structural and Multidisciplinary Optimization 1 Statistical Applications in Genetics and Molecular Biology 1 International Journal of Numerical Analysis and Modeling 1 Lecture Notes in Computational Science and Engineering 1 Foundations and Trends in Machine Learning 1 Journal of Computational and Graphical Statistics 1 Statistics and Computing 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Cited in 20 Fields 82 Numerical analysis (65-XX) 22 Operations research, mathematical programming (90-XX) 13 Computer science (68-XX) 12 Mechanics of deformable solids (74-XX) 11 Partial differential equations (35-XX) 7 Fluid mechanics (76-XX) 5 Statistics (62-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Mechanics of particles and systems (70-XX) 3 Information and communication theory, circuits (94-XX) 2 Combinatorics (05-XX) 2 Ordinary differential equations (34-XX) 2 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Citations by Year