Lanczos algorithm
E697941
The Lanczos algorithm is an iterative numerical method used to approximate eigenvalues and eigenvectors of large sparse matrices, particularly in scientific computing and numerical linear algebra.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
Krylov subspace method
ⓘ
iterative method ⓘ numerical algorithm ⓘ |
| application |
electronic structure calculations
ⓘ
graph partitioning ⓘ information retrieval ⓘ model reduction ⓘ principal component analysis ⓘ quantum many-body problems ⓘ structural engineering ⓘ vibration analysis ⓘ |
| basedOn | Krylov subspace NERFINISHED ⓘ |
| computes | orthonormal basis of Krylov subspace ⓘ |
| field |
computational chemistry
ⓘ
computational physics ⓘ numerical linear algebra ⓘ scientific computing ⓘ |
| hasVariant |
block Lanczos method
NERFINISHED
ⓘ
implicitly restarted Lanczos method ⓘ thick-restart Lanczos method NERFINISHED ⓘ |
| implementedIn |
ARPACK
NERFINISHED
ⓘ
MATLAB eigs function ⓘ SLEPc NERFINISHED ⓘ SciPy sparse.linalg.eigsh NERFINISHED ⓘ |
| inputType |
Hermitian matrix
ⓘ
large sparse matrix ⓘ symmetric matrix ⓘ |
| namedAfter | Cornelius Lanczos NERFINISHED ⓘ |
| outputType |
Ritz values
ⓘ
Ritz vectors ⓘ tridiagonal matrix ⓘ |
| property |
matrix-free
ⓘ
memory efficient for large sparse problems ⓘ sensitive to loss of orthogonality ⓘ short-term recurrence ⓘ well-suited for extreme eigenvalues ⓘ |
| purpose |
approximation of eigenvalues of large sparse matrices
ⓘ
approximation of eigenvectors of large sparse matrices ⓘ reduction of large symmetric matrices to tridiagonal form ⓘ |
| relatedTo |
Arnoldi iteration
NERFINISHED
ⓘ
Rayleigh–Ritz method NERFINISHED ⓘ conjugate gradient method NERFINISHED ⓘ power method ⓘ |
| requires |
initial starting vector
ⓘ
matrix-vector products ⓘ |
| uses | three-term recurrence ⓘ |
| yearIntroduced | 1950 ⓘ |
Referenced by (1)
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