testmatrix swMATH ID: 14347 Software Authors: N.J. Higham Description: The Test Matrix Toolbox for MATLAB. We describe version 3.0 of the Test Matrix Toolbox for Matlab 4.2. The toolbox contains a collection of test matrices, routines for visualizing matrices, routines for direct search optimization, and miscellaneous routines that provide useful additions to Matlab’s existing set of functions. There are 58 parametrized test matrices, which are mostly square, dense, nonrandom, and of arbitrary dimension. The test matrices include ones with known inverses or known eigenvalues; ill-conditioned or rank deficient matrices; and symmetric, positive definite, orthogonal, defective, involutary, and totally positive matrices. The visualization routines display surface plots of a matrix and its (pseudo-) inverse, the field of values, Gershgorin disks, and two- and three-dimensional views of pseudospectra. The direct search optimization routines implement the alternating directions method, the multidirectional search method and the Nelder–Mead simplex method. Homepage: https://github.com/carandraug/testmatrix/blob/master/Test%20Matrix%20Toolbox/matrix.m Source Code: https://github.com/carandraug/testmatrix/blob/master/Test%20Matrix%20Toolbox/matrix.m Dependencies: Matlab Related Software: mctoolbox; CONTEST; mftoolbox; Matlab; Eigtool; LAPACK; Algorithm 694; MATLAB expm; Seigtool; ARPACK; SparseMatrix; CUBLAS; CUDA; JDQZ; JDQR; Harwell-Boeing sparse matrix collection; MatrixMarket; Matrix Depot; Regularization tools; advanpix Cited in: 84 Publications all top 5 Cited by 105 Authors 14 Higham, Nicholas J. 7 Defez, Emilio 7 Ibáñez González, Jacinto Javier 7 Sastre, Jorge 5 Higham, Desmond J. 5 Peinado, Jesús 4 Alonso, Pedro 4 Benzi, Michele 4 Simoncini, Valeria 3 Brezinski, Claude 3 Chang, Xiaowen 3 Wu, Gang 2 Alonso-Jordá, Pedro 2 Arrigo, Francesca 2 Bai, Zhaojun 2 Bekas, Constantine 2 Boito, Paola 2 Braconnier, Thierry 2 Cox, Anthony J. 2 Delgado, Jorge F. M. 2 Duff, Iain S. 2 Gallopoulos, Efstratios 2 Gemignani, Luca 2 Golub, Gene Howard 2 Grindrod, Peter 2 Lavallée, P.-F. 2 Noferini, Vanni 2 Oste, Roy 2 Peña, Juan Manuel 2 Redivo-Zaglia, Michela 2 Ruiz, Pedro A. 2 Tisseur, Françoise 2 Van der Jeugt, Joris 2 Wei, Yimin 2 Zhang, Ying 1 Arioli, Mario 1 Bhuruth, Muddun 1 Brühl, Martin 1 Burrage, Kevin 1 Carvalho, João B. 1 Chaitin-Chatelin, Françoise 1 Cheng, Sheung Hun 1 Datta, Biswa N. 1 Davies, Philip I. 1 Edelman, Alan Stuart 1 Eidelman, Yuli 1 Fahey, Mark R. 1 Fasi, Massimiliano 1 Fatemi, Masoud 1 Fenu, Caterina 1 Foster, Leslie V. 1 Gallego, Rafael 1 Gallestey Alvarez, Eduardo 1 Gallestey, Eduardo 1 Godunov, Sergeĭ Konstantinovich 1 Gopaul, Ashvin 1 Grammont, Laurence 1 Gu, Chuanqing 1 Guarracino, Mario Rosario 1 Guo, Yongyan 1 Hayami, Ken 1 Knight, Philip A. 1 Koikari, Souji 1 Kokiopoulou, Efrosini 1 Kostlan, Eric 1 Kuhlemann, Verena 1 Largillier, Alain 1 Lee, Steven L. 1 Lehoucq, Richard B. 1 Li, Wen 1 Liao, Zeyu 1 Liu, Xinguo 1 Lu, Chengbo 1 Luo, ZiYan 1 Mantzaris, Alexander V. 1 Mikaitis, Mantas 1 Morikuni, Keiichi 1 Munarini, Emanuele 1 Musschoot, C. 1 Paige, Christopher C. 1 Peña, Guillermo 1 Perla, Francesca 1 Polyak, Boris Teodorovich 1 Qi, Liqun 1 Rodriguez, Giuseppe 1 Sadkane, Miloud 1 Santiago, Cosmo Damião 1 Shcherbakov, Pavel Sergeevich 1 Sidje, Roger B. 1 Singer, Sanja 1 Singer, Saša 1 Sjöström, Eva 1 Sorensen, Danny C. 1 Szyld, Daniel B. 1 Torri, Damiano 1 Van Dooren, Paul M. 1 Vömel, Christof 1 Vong, Seakweng 1 Watkins, David S. 1 Xie, Ze-Jia ...and 5 more Authors all top 5 Cited in 29 Serials 11 Journal of Computational and Applied Mathematics 11 SIAM Journal on Matrix Analysis and Applications 8 BIT 8 Linear Algebra and its Applications 6 Numerical Algorithms 5 Applied Mathematics and Computation 4 SIAM Journal on Scientific Computing 4 Numerical Linear Algebra with Applications 2 Numerische Mathematik 2 Applied Numerical Mathematics 1 Computers & Mathematics with Applications 1 IMA Journal of Numerical Analysis 1 Journal of the Franklin Institute 1 Mathematics of Computation 1 Computing 1 Theoretical Computer Science 1 Parallel Computing 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 Japan Journal of Industrial and Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Computational Optimization and Applications 1 ETNA. Electronic Transactions on Numerical Analysis 1 Annals of Numerical Mathematics 1 Advances in Computational Mathematics 1 Chaos 1 Data Mining and Knowledge Discovery 1 International Journal of Applied Mathematics and Computer Science 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications all top 5 Cited in 19 Fields 72 Numerical analysis (65-XX) 28 Linear and multilinear algebra; matrix theory (15-XX) 8 Combinatorics (05-XX) 5 Computer science (68-XX) 3 Ordinary differential equations (34-XX) 3 Operations research, mathematical programming (90-XX) 2 Special functions (33-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year