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Uniform Error Estimates for the Lanczos Method [PDF]
SIAM Journal on Matrix Analysis and Applications, 2021 The Lanczos method is one of the most powerful and fundamental techniques for solving an extremal symmetric eigenvalue problem. Convergence-based error estimates depend heavily on the eigenvalue gap. In practice, this gap is often relatively small, resulting in significant overestimates of error.
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Quantum finite-temperature Lanczos method
Physical Review ResearchThe computation of thermal properties of quantum many-body systems is a central challenge in our understanding of quantum mechanics. We introduce the quantum finite-temperature Lanczos method (QFTLM), which extends the finite-temperature Lanczos method ...
Gian Gentinetta +3 more
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New implementations of Lanczos method
Journal of Computational and Applied Mathematics, 1995 The author discusses a class of iterative solution methods for linear systems, based on formal orthogonal polynomials. As special cases it contains several implementations of the Lanczos method. He discusses some other implementations and compares them in the case of a matrix arising from the 5-point discretization of a 2-dimensional partial ...
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Exact and efficient Lanczos method on a quantum computer [PDF]
Quantum, 2023 We present an algorithm that uses block encoding on a quantum computer to exactly construct a Krylov space, which can be used as the basis for the Lanczos method to estimate extremal eigenvalues of Hamiltonians.
William Kirby +2 more
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Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices
Mathematics, 2021 The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude.
Anna Concas +3 more
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The improvement of sparsity gravity inversion using an adaptive lanczos bidiagonalization method
Frontiers in Earth Science, 2023 Inversion of gravity data is one the important steps in the interpretation of practical data. The detection of sharp boundaries between anomalous bodies and host rocks is an interesting point in the geological frameworks.
Meng Zhaohai +7 more
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Numerical stability of Lanczos methods [PDF]
Nuclear Physics B - Proceedings Supplements, 2000 The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature.
Cahill, Eamonn +4 more
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IEEE Access, 2023 In this paper, the symmetric Lanczos algorithm and mixed finite element method are combined to improve the efficiency and accuracy of S-parameter simulation in a broad frequency band.
Ke Chen +4 more
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Condition number estimation of preconditioned matrices. [PDF]
PLoS ONE, 2015 The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results.
Noriyuki Kushida
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Orthogonal polynomials and the Lanczos method [PDF]
Banach Center Publications, 1994 Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir , Orthomin,
Brezinski C. +2 more
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