ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems. The package is designed to compute a few eigenvalues and corresponding eigenvectors of a general n by n matrix A. It is most appropriate for large sparse or structured matrices A where structured means that a matrix-vector product w <- Av requires order n rather than the usual order n2 floating point operations. This software is based upon an algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi Method (IRAM). When the matrix A is symmetric it reduces to a variant of the Lanczos process called the Implicitly Restarted Lanczos Method (IRLM). These variants may be viewed as a synthesis of the Arnoldi/Lanczos process with the Implicitly Shifted QR technique that is suitable for large scale problems. For many standard problems, a matrix factorization is not required. Only the action of the matrix on a vector is needed. ARPACK software is capable of solving large scale symmetric, nonsymmetric, and generalized eigenproblems from significant application areas. The software is designed to compute a few (k) eigenvalues with user specified features such as those of largest real part or largest magnitude. Storage requirements are on the order of n*k locations. No auxiliary storage is required. A set of Schur basis vectors for the desired k-dimensional eigen-space is computed which is numerically orthogonal to working precision. Numerically accurate eigenvectors are available on request.

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  1. Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
  2. Adam, Lukáš; Hintermüller, Michael; Peschka, Dirk; Surowiec, Thomas M.: Optimization of a multiphysics problem in semiconductor laser design (2019)
  3. Andreotti, Eleonora; Edelmann, Dominik; Guglielmi, Nicola; Lubich, Christian: Constrained graph partitioning via matrix differential equations (2019)
  4. Aravkin, Aleksandr Y.; Burke, James V.; Drusvyatskiy, Dmitry; Friedlander, Michael P.; Roy, Scott: Level-set methods for convex optimization (2019)
  5. Avron, Haim; Druinsky, Alex; Toledo, Sivan: Spectral condition-number estimation of large sparse matrices. (2019)
  6. Benner, Peter; Mitchell, Tim: Extended and improved criss-cross algorithms for computing the spectral value set abscissa and radius (2019)
  7. Boffi, Daniele; Gastaldi, Lucia; Rodríguez, Rodolfo; Šebestová, Ivana: A posteriori error estimates for Maxwell’s eigenvalue problem (2019)
  8. Brynjell-Rahkola, Mattias; Hanifi, Ardeshir; Henningson, Dan S.: On the stability of a Blasius boundary layer subject to localised suction (2019)
  9. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: An implicit filter for rational Krylov using core transformations (2019)
  10. De Marchi, S.; Martínez, A.; Perracchione, E.: Fast and stable rational RBF-based partition of unity interpolation (2019)
  11. Erichson, N. Benjamin; Mathelin, Lionel; Kutz, J. Nathan; Brunton, Steven L.: Randomized dynamic mode decomposition (2019)
  12. Giannakis, Dimitrios; Ourmazd, Abbas; Slawinska, Joanna; Zhao, Zhizhen: Spatiotemporal pattern extraction by spectral analysis of vector-valued observables (2019)
  13. Giordano, Matteo: Localisation in 2+1 dimensional SU(3) pure gauge theory at finite temperature (2019)
  14. Hou, Thomas Y.; Huang, De; Lam, Ka Chun; Zhang, Ziyun: A fast hierarchically preconditioned eigensolver based on multiresolution matrix decomposition (2019)
  15. Huang, Wei-Qiang; Lin, Wen-Wei; Lu, Henry Horng-Shing; Yau, Shing-Tung: iSIRA: integrated shift-invert residual Arnoldi method for graph Laplacian matrices from big data (2019)
  16. Lackner, C.; Meng, S.; Monk, P.: Determination of electromagnetic Bloch variety in a medium with frequency-dependent coefficients (2019)
  17. Lambers, James V.; Sumner, Amber C.: Explorations in numerical analysis (2019)
  18. Li, Ruipeng; Xi, Yuanzhe; Erlandson, Lucas; Saad, Yousef: The eigenvalues slicing library (EVSL): algorithms, implementation, and software (2019)
  19. Manguoğlu, Murat; Mehrmann, Volker: A robust iterative scheme for symmetric indefinite systems (2019)
  20. Matteo Ravasi, Ivan Vasconcelos: PyLops - A Linear-Operator Python Library for large scale optimization (2019) arXiv

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