ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods

By R. Lehoucq, Danny C. Sorensen, Chao Yang. 1998

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

Gradient Descent Happens in a Tiny Subspace (2018, methodology): “For example, to compute the top eigenvectors of the Hessian efficiently, we used the Lanczos method (Lehoucq et al., 1998), which relies on repeatedly computing the Hessian-vector product Hv for some vector v.”
Network Embedding as Matrix Factorization: Unifying DeepWalk, LINE, PTE, and node2vec (2017, methodology): “In our algorithm, we first approximate D − 1 / 2 AD − 1 / 2 with its top-h h Since only top-h eigenpairs are required and the matrix is sparse, we can perform decomposition using the Arnoldi method [19] which achieves significant time reduction [45].”
Free vibration analysis of ribbed plates by a combined analytical-numerical method (2009, methodology): “An algorithmic variant of the Arnoldi process called the Implicitly Restarted Arnoldi method is freely available within the FORTRAN package ARPACK [22].”
Learning Effective and Interpretable Semantic Models using Non-Negative Sparse Embedding (2012, methodology): “this step we used Python/Scipy implementation of the Implicitly Restarted Arnoldi method (Lehoucq et al., 1998; Jones et al., 2001) which was coherent with the PPMI normalization used, since a zero value represented both negative target-feature associations, and those that were not observed or fell ”
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems (2000, methodology): “This stopping test differs from earlier ones in that it takes into account of the orthogonality of Q [5, 12].”
SLEPc: A scalable and flexible toolkit for the solution of eigenvalue problems (2005, methodology): “The most complete of these libraries is ARPACK [Lehoucq et al. 1998], which implements the Arnoldi/Lanczos process with Implicit Restart for standard and generalized problems, in both real and complex arithmetic.”
Vector Finite Difference Modesolver for Anisotropic Dielectric Waveguides (2008, methodology): “The eigenmodes of the waveguide were calculated using an iterative shift-invert sparse matrix eigenvector solver(ARPACK [ 23 ])providedthroughabuilt-inMATLABfunction(eigs.)This routine uses an iterative Lanczos method to compute the largest eigenvalues and corresponding eigenvectors of the shifted m”
Convergence Guarantees for RMSProp and ADAM in Non-Convex Optimization and an Empirical Comparison to Nesterov Acceleration (2018, background): “eigsh that can use a function that computes the matrix-vector products to compute the eigenvalues of the matrix [23].”
Origin of transonic buffet on aerofoils (2007, methodology): “This is achieved using the ARPACK routines (Lehoucq et al. 1998) with the shift–invert mode.”