IR Tools swMATH ID: 26721 Software Authors: Gazzola, Silvia; Hansen, Per Christian; Nagy, James G. Description: IR Tools: A MATLAB Package of Iterative Regularization Methods and Large-Scale Test Problems. This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called IR Tools, serves two related purposes: we provide implementations of a range of iterative solvers, including several recently proposed methods that are not available elsewhere, and we provide a set of large-scale test problems in the form of discretizations of 2D linear inverse problems. The solvers include iterative regularization methods where the regularization is due to the semi-convergence of the iterations, Tikhonov-type formulations where the regularization is explicitly formulated in the form of a regularization term, and methods that can impose bound constraints on the computed solutions. All the iterative methods are implemented in a very flexible fashion that allows the problem’s coefficient matrix to be available as a (sparse) matrix, a function handle, or an object. The most basic call to all of the various iterative methods requires only this matrix and the right hand side vector; if the method uses any special stopping criteria, regularization parameters, etc., then default values are set automatically by the code. Moreover, through the use of an optional input structure, the user can also have full control of any of the algorithm parameters. The test problems represent realistic large-scale problems found in image reconstruction and several other applications. Numerical examples illustrate the various algorithms and test problems available in this package. Homepage: https://arxiv.org/abs/1712.05602 Source Code: https://github.com/jnagy1/IRtools Dependencies: Matlab Keywords: Numerical Analysis; arXiv_math.NA; MATLAB; Iterative Regularization; test problems; large-scale Related Software: Regularization tools; AIR tools; LSQR; UTV; CRAIG; RestoreTools; HyBR; Matlab; LSMR; ErresTools; GKB-FP; mftoolbox; LSRN; JDQR; JDQZ; rrgmrestbx; GitHub; ASTRA; SparseMatrix; PROPACK Cited in: 84 Documents Standard Articles 2 Publications describing the Software, including 1 Publication in zbMATH Year IR tools: a MATLAB package of iterative regularization methods and large-scale test problems. Zbl 1415.65003Gazzola, Silvia; Hansen, Per Christian; Nagy, James G. 2019 IR Tools: A MATLAB Package of Iterative Regularization Methods and Large-Scale Test Problems arXiv Silvia Gazzola, Per Christian Hansen, James G. Nagy 2017 all top 5 Cited by 140 Authors 13 Reichel, Lothar 11 Buccini, Alessandro 11 Gazzola, Silvia 11 Nagy, James Gerard 7 Chung, Julianne M. 5 Donatelli, Marco 5 Jia, Zhongxiao 4 Jiang, Jiahua 4 Pasha, Mirjeta 4 Saibaba, Arvind Krishna 3 de Sturler, Eric 3 Meng, Chang 3 Renaut, Rosemary Anne 3 Webber, James W. 2 Alqahtani, Abdulaziz 2 Bai, Xianglan 2 Cornelis, Jeffrey 2 Español, Malena I. 2 Hansen, Per Christian 2 Herring, James L. 2 Kilmer, Misha Elena 2 Kindermann, Stefan 2 Li, Haibo 2 Luiken, Nick 2 Miller, Eric L. 2 Novati, Paolo 2 Onisk, Lucas 2 Ramlau, Ronny 2 Ruthotto, Lars 2 Sabaté Landman, Malena 2 van Leeuwen, Tristan 2 Vanroose, Wim 2 Wei, Yimin 2 Xi, Yuanzhe 2 Yu, Bo 1 Abe, Kuniyoshi 1 Aeron, Shuchin 1 Aleotti, Stefano 1 Alvarruiz, Fernando 1 Andersen, Martin S. 1 Antil, Harbir 1 Arıkan, Orhan 1 Bai, Zhengjian 1 Bardsley, Johnathan M. 1 Beik, Fatemeh Panjeh Ali 1 Benzi, Michele 1 Berer, Thomas 1 Bianchi, Davide 1 Bolten, Matthias 1 Burgholzer, Peter 1 Byrne, Michael J. 1 Campos, Carmen 1 Caruso, Noe Angelo 1 Castañeda, Victor 1 Chang, Weike 1 Chen, Xiaotong 1 Chen, Zixuan 1 Cho, Taewon 1 Cho, Yeol Je 1 Chung, Matthias 1 Cipolla, Stefano 1 Courdurier, Matias 1 Cueva, Evelyn 1 Dai, Hua 1 D’Ascenzo, Nicola 1 Debarre, Thomas 1 Donati, Laurène 1 Dong, Yiqiu 1 Durastante, Fabio 1 Effland, Alexander 1 Ferrari, Paola 1 Fung, Samy Wu 1 Garvey, Larissa 1 George, Santhosh 1 Haber, Eldad 1 Härtel, Steffen 1 Helmstetter, Anthony W. 1 Higham, Nicholas John 1 Hu, Yunyi 1 Huang, Guang-Xin 1 Huemer, Mario 1 Hussey, Erika 1 Hutterer, Victoria 1 Jidesh, P. 1 Jozi, Meisam 1 Karimi, Saeed 1 Karimpour, Mehdi 1 Kobler, Erich 1 Kovács, Peter 1 Kunisch, Karl 1 Lang, Oliver 1 Lei, Xiaojun 1 Lou, Yifei 1 Mach, Thomas 1 MacLachlan, Scott P. 1 McCann, Michael T. 1 Mekoth, Chitra 1 Michelangeli, Alessandro 1 Mikaitis, Mantas 1 Miller, Scot M. ...and 40 more Authors all top 5 Cited in 25 Serials 14 Inverse Problems 11 Numerical Algorithms 10 SIAM Journal on Scientific Computing 8 ETNA. Electronic Transactions on Numerical Analysis 6 Applied Numerical Mathematics 5 Journal of Computational and Applied Mathematics 4 Numerical Linear Algebra with Applications 3 BIT 3 SIAM Journal on Matrix Analysis and Applications 2 Calcolo 2 Journal of Scientific Computing 2 Inverse Problems and Imaging 2 SIAM Journal on Imaging Sciences 1 Computers & Mathematics with Applications 1 Journal of Mathematical Analysis and Applications 1 Journal of Computational Mathematics 1 Communications in Statistics. Theory and Methods 1 Linear Algebra and its Applications 1 SIAM Review 1 Journal of Mathematical Imaging and Vision 1 The Journal of Analysis 1 Advances in Computational Mathematics 1 Sampling Theory in Signal and Image Processing 1 Computational Science & Engineering 1 East Asian Journal on Applied Mathematics all top 5 Cited in 19 Fields 78 Numerical analysis (65-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 13 Information and communication theory, circuits (94-XX) 12 Computer science (68-XX) 9 Operations research, mathematical programming (90-XX) 6 Operator theory (47-XX) 6 Biology and other natural sciences (92-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Statistics (62-XX) 4 Partial differential equations (35-XX) 4 Integral equations (45-XX) 2 Integral transforms, operational calculus (44-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX) Citations by Year