Advances in Nuclear Physics 1977
DOI: 10.1007/978-1-4615-8234-2_2
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Computational Methods for Shell-Model Calculations

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Cited by 181 publications
(121 citation statements)
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“…by the Lanczos algorithm [26,27]. Within this framework I use two different model spaces and interactions.…”
Section: Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…by the Lanczos algorithm [26,27]. Within this framework I use two different model spaces and interactions.…”
Section: Methodsmentioning
confidence: 99%
“…I carry out the Lanczos algorithm with |Ψ as my pivot, that is the starting vector |v 1 : As is well-known for the Lanczos algorithm [27], this procedure generates a Krylov subspace and the eigenvalues of the tridiagonal matrix given by α i , β i will converge to the extremal eigenpairs ofL 2 , of which the eigenvectors are a linear combination of the Lanczos vectors,…”
Section: A L-s Decompositionmentioning
confidence: 99%
“…• Extension to larger ladders and systems of higher space dimensions with the help of more sophisticated numerical algorithms [27,28].…”
Section: Discussionmentioning
confidence: 99%
“…Because one is generally interested only in low-lying states, typically the lowest 5-20 states, one can use Arnoldi methods such as the Lanczos algorithm [12,13], where one iteratively transforms the Hamiltonian to tridiagonal form:…”
Section: Introductionmentioning
confidence: 99%
“…the extremal eigenvalues converge quickly [13], which one can understand through the lens of the classical moments problem [14]. The downside of Lanczos is that, due to numerical round-off error the Lanczos vectors |v n lose orthogonality and must be forcibly orthonormalized, which is why Householder is often preferred when one must completely transform a matrix to tridiagonal form.…”
Section: Introductionmentioning
confidence: 99%