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. Bastian, Peter; Scheichl, Robert; Seelinger, Linus; Strehlow, Arne: Multilevel spectral domain decomposition (2022)
  2. Boureghda, Abdelouahab; Choutri, Abdelaziz; Rezgui, Hayat: On domain error truncation in a problem of guided modes computation in optical fibers (2022)
  3. Engström, C.; Giani, S.; Grubišić, L.: Higher order composite DG approximations of Gross-Pitaevskii ground state: benchmark results and experiments (2022)
  4. Faugaret, Antoine; Duguet, Yohann; Fraigneau, Yann; Martin Witkowski, Laurent: A simple model for arbitrary pollution effects on rotating free-surface flows (2022)
  5. Lampe, Jörg; Voss, Heinrich: A survey on variational characterizations for nonlinear eigenvalue problems (2022)
  6. Peralta, Gilbert; Kunisch, Karl: Mixed and hybrid Petrov-Galerkin finite element discretization for optimal control of the wave equation (2022)
  7. Petrov, M.; Utyuzhnikov, S.; Chikitkin, A.; Smirnova, N.: Extension of near-wall domain decomposition to modeling flows with laminar-turbulent transition (2022)
  8. Pfister, J.-L.; Fabbiane, N.; Marquet, O.: Global stability and resolvent analyses of laminar boundary-layer flow interacting with viscoelastic patches (2022)
  9. Rontsis, Nikitas; Goulart, Paul; Nakatsukasa, Yuji: Efficient semidefinite programming with approximate ADMM (2022)
  10. Souto, Mario; Garcia, Joaquim D.; Veiga, Álvaro: Exploiting low-rank structure in semidefinite programming by approximate operator splitting (2022)
  11. Abrate, N.; Burrone, M.; Dulla, S.; Ravetto, P.; Saracco, P.: Eigenvalue formulations for the \textit(P_N) approximation to the neutron transport equation (2021)
  12. Achdou, Yves; Laurière, Mathieu; Lions, Pierre-Louis: Optimal control of conditioned processes with feedback controls (2021)
  13. Aimi, A.; Desiderio, L.; Fedeli, P.; Frangi, A.: A fast boundary-finite element approach for estimating anchor losses in micro-electro-mechanical system resonators (2021)
  14. Al Daas, Hussam; Grigori, Laura; Jolivet, Pierre; Tournier, Pierre-Henri: A multilevel Schwarz preconditioner based on a hierarchy of robust coarse spaces (2021)
  15. Arndt, Daniel; Bangerth, Wolfgang; Blais, Bruno; Fehling, Marc; Gassmöller, Rene; Heister, Timo; Heltai, Luca; Köcher, Uwe; Kronbichler, Martin; Maier, Matthias; Munch, Peter; Pelteret, Jean-Paul; Proell, Sebastian; Simon, Konrad; Turcksin, Bruno; Wells, David; Zhang, Jiaqi: The \textttdeal.II library, Version 9.3 (2021)
  16. Barnafi, Nicolás; Zunino, Paolo; Dedè, Luca; Quarteroni, Alfio: Mathematical analysis and numerical approximation of a general linearized poro-hyperelastic model (2021)
  17. Bootland, Niall; Dolean, Victorita; Jolivet, Pierre; Tournier, Pierre-Henri: A comparison of coarse spaces for Helmholtz problems in the high frequency regime (2021)
  18. Courrieu, Pierre: On the convergence of rank-one multi-target linear regression (2021)
  19. Cowen, Lenore; Devkota, Kapil; Hu, Xiaozhe; Murphy, James M.; Wu, Kaiyi: Diffusion state distances: multitemporal analysis, fast algorithms, and applications to biological networks (2021)
  20. Giani, Stefano; Hakula, Harri: On effects of perforated domains on parameter-dependent free vibration (2021)

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