CIRR swMATH ID: 12618 Software Authors: Sakurai, Tetsuya; Tadano, Hiroto Description: CIRR: a Rayleigh-Ritz method with contour integral for generalized eigenvalue problems. We consider a Rayleigh-Ritz type eigensolver for finding a limited set of eigenvalues and their corresponding eigenvectors in a certain region of generalized eigenvalue problems. When the matrices are very large, iterative methods are used to generate an invariant subspace that contains the desired eigenvectors. Approximations are extracted from the subspace through a Rayleigh-Ritz projection. In this paper, we present a Rayleigh-Ritz type method with a contour integral (CIRR method). In this method, numerical integration along a circle that contains relatively small number of eigenvalues is used to construct a subspace. Since the process to derive the subspace can be performed in parallel, the presented method is suitable for master-worker programming models. Numerical experiments illustrate the property of the proposed method. Homepage: http://projecteuclid.org/euclid.hokmj/1272848031 Keywords: generalized eigenvalue problem; Rayleigh–Ritz method; contour integral; eigenvectors Related Software: FEAST; SparseMatrix; ARPACK; JDQZ; LAPACK; EVSL; JDQR; PRIMME; PARDISO; MatrixMarket; UMFPACK; PARSEC; Tensorlab; NLEVP; lobpcg.m; BLOPEX; SLEPc; JADAMILU; Anasazi; Complex Optimization Toolbox Cited in: 44 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year CIRR: a Rayleigh-Ritz method with contour integral for generalized eigenvalue problems. Zbl 1156.65035Sakurai, Tetsuya; Tadano, Hiroto 2007 all top 5 Cited by 88 Authors 13 Sakurai, Tetsuya 8 Imakura, Akira 5 Tadano, Hiroto 5 Yin, Guojian 4 Ikegami, Tsutomu 4 Saad, Yousef 4 Xi, Yuanzhe 3 Du, Lei 3 Morikuni, Keiichi 3 Polizzi, Eric 2 Alvermann, Andreas 2 Austin, Anthony P. 2 Chan, Raymond Hon-Fu 2 Chen, Xiaoping 2 Dai, Hua 2 Fehske, Holger 2 Galgon, Martin 2 Hager, Georg 2 Kravanja, Peter 2 Kreutzer, Moritz 2 Lang, Bruno 2 Nagashima, Umpei 2 Takayasu, Akitoshi 2 Tang, Ping Tak Peter 2 Trefethen, Lloyd Nicholas 2 Van Barel, Marc 2 Wellein, Gerhard 1 Asakura, Junko 1 Bai, Zhaojun 1 Balakrishnan, Venkataramanan 1 Basermann, Achim 1 Bientinesi, Paolo 1 Bungartz, Hans-Joachim 1 Carbogno, Christian 1 Cauley, Stephen 1 Di Napoli, Edoardo A. 1 Erlandson, Lucas 1 Ernst, Dominik 1 Futamura, Yasunori 1 Güttel, Stefan 1 Horesh, Lior 1 Huang, Tsungming 1 Huber, Sarah E. 1 Huckle, Thomas Kilian 1 Ida, Akihiro 1 Jia, Zhongxiao 1 Kalantzis, Vassilis 1 Kawai, Masatoshi 1 Kestyn, James 1 Knyazev, Andrew V. 1 Köcher, Simone 1 Kollnig, Konrad 1 Kuramashi, Yoshinobu 1 Kus, Pavel 1 Lederer, Hermann 1 Li, Ruipeng 1 Liao, Weichien 1 Manguoglu, Murat 1 Manin, Valeriy 1 Marek, Andreas 1 Mehrmann, Volker 1 Meng, Shuangshuang 1 Murakami, Hiroshi 1 Najafi, H. Saberi 1 Nakajima, Kengo 1 Nedamani, F. Abbasi 1 Nemec, Lydia 1 Ohno, Hiroshi 1 Pieper, Andreas 1 Reuter, Karsten 1 Rippl, Michael 1 Röhrig-Zöllner, Melven 1 Scheffler, Matthias 1 Scheurer, Christoph 1 Senzaki, Kenta 1 Shahzad, Faisal 1 Simoes Brambila, Danilo 1 Thies, Jonas 1 Vecharynski, Eugene 1 Viaud, Gautier 1 Wang, Weichung 1 Xia, Jianlin 1 Xiao, Jinyou 1 Ye, Xin 1 Yeung, Man-Chung 1 Zhang, Chuanzeng 1 Zhang, Kailiang 1 Zheng, Changjun all top 5 Cited in 17 Serials 10 SIAM Journal on Scientific Computing 6 Journal of Computational and Applied Mathematics 3 Journal of Scientific Computing 3 Japan Journal of Industrial and Applied Mathematics 3 Numerical Algorithms 3 Taiwanese Journal of Mathematics 2 Applied Mathematics and Computation 2 SIAM Journal on Matrix Analysis and Applications 2 Linear Algebra and its Applications 2 JSIAM Letters 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 Hokkaido Mathematical Journal 1 SIAM Journal on Numerical Analysis 1 Applied Mathematics Letters 1 Numerical Linear Algebra with Applications 1 Mathematical Problems in Engineering all top 5 Cited in 14 Fields 44 Numerical analysis (65-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 3 Functions of a complex variable (30-XX) 3 Approximations and expansions (41-XX) 3 Operator theory (47-XX) 2 Partial differential equations (35-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 Ordinary differential equations (34-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year