Compression of unitary rank--structured matrices to CMV-like shape with an application to polynomial rootfinding [PDF]
, 2013 This paper is concerned with the reduction of a unitary matrix U to CMV-like shape. A Lanczos--type algorithm is presented which carries out the reduction by computing the block tridiagonal form of the Hermitian part of U, i.e., of the matrix U+U^H.
Bevilacqua, Roberto +2 more
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Lippmann–Schwinger–Lanczos algorithm for inverse scattering problems [PDF]
Inverse Problems, 2021 Abstract Data-driven reduced order models (ROMs) are combined with the Lippmann–Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization. Embedding into the continuous problem, a data-driven internal solution is produced.
V Druskin, S Moskow, M Zaslavsky
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Incremental eigenpair computation for graph Laplacian matrices: theory and applications [PDF]
, 2017 The smallest eigenvalues and the associated eigenvectors (i.e., eigenpairs) of a graph Laplacian matrix have been widely used for spectral clustering and community detection. However, in real-life applications, the number of clusters or communities (say,
Al Hasan, Mohammad +2 more
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The Lanczos algorithm and complex Gauss quadrature [PDF]
ETNA - Electronic Transactions on Numerical Analysis, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pozza S, Pranic MS, Strakos Z
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Krylov complexity and orthogonal polynomials
Nuclear Physics B, 2022 Krylov complexity measures operator growth with respect to a basis, which is adapted to the Heisenberg time evolution. The construction of that basis relies on the Lanczos algorithm, also known as the recursion method.
Wolfgang Mück, Yi Yang
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The Lanczos algorithm with partial reorthogonalization [PDF]
Mathematics of Computation, 1984 The Lanczos algorithm is becoming accepted as a powerful tool for finding the eigenvalues and for solving linear systems of equations. Any practical implementation of the algorithm suffers however from roundoff errors, which usually cause the Lanczos vectors to lose their mutual orthogonality.
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An alternative implementation of the Lanczos algorithm for wave function propagation [PDF]
, 2006 We reformulate the Lanczos algorithm for quantum wave function propagation in terms of variational principle. By including some basis states of previous time steps into the variational subspace, the resultant accuracy increases by several orders ...
Jie, Quanlin, Liu, Dunhuan
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Computational Methods for UV-Suppressed Fermions [PDF]
, 2002 Lattice fermions with suppressed high momentum modes solve the ultraviolet slowing down problem in lattice QCD. This paper describes a stochastic evaluation of the effective action of such fermions.
Artan Boriçi +18 more
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Restarting from Specific Points to Cure Breakdown in Lanczos-type Algorithms
Journal of Mathematical and Fundamental Sciences, 2015 Breakdown in Lanczos-type algorithms is a common phenomenon which is due to the non-existence of some orthogonal polynomials. It causes the solution process to halt.
Maharani, Abdellah Salhi
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Partition of unity interpolation using stable kernel-based techniques [PDF]
, 2016 In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets.
Cavoretto, R. +4 more
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