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Lanczos algorithm

The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the m {\displaystyle m} "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an n × n {\displaystyle n\times n} Hermitian matrix, where m {\displaystyle m} is often but not necessarily much smaller…

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Overview

The algorithm

Derivation of the algorithm

Convergence and other dynamics

Variations

Applications

Implementations

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Lanczos algorithm

Nodes82
Edges81
Triples67
Avg. degree1.98
Density0.02439
Components1

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Lanczos algorithm

Top relations

related to Variations · 10
Lanczos algorithm → Another, ARPACK, Lanczos, Many, One, These, Thick-Restart Lanczos, This, TRLan, Variations
related to Implementations · 9
Lanczos algorithm → ARPACK, FORTRAN, GNU Octave, Julia, Lanczos, MATLAB, Python, SciPy, The NAG Library
has application · 8
Lanczos algorithm → Eigenvectors, Google, Hamiltonians, HITS, Jon Kleinberg, Lanczos, PageRank, Since
related to Application to tridiagonalization · 8
Lanczos algorithm → Aspects, During, Householder, Interest, Kaniel, Lanczos, Paige, Though
related to Kaniel–Paige convergence theory · 8
Lanczos algorithm → After, Convergence, Conversely, Krylov, Lanczos, Rayleigh, Since, The
related to Numerical stability · 7
Lanczos algorithm → As, For, However, Lanczos, Numerical, Stability, Therefore
related to Application to the eigenproblem · 6
Lanczos algorithm → If, Lanczos, Nonetheless, The Lanczos, Tx, Vx
related to Nullspace over a finite field · 4
Lanczos algorithm → GF, In, Lanczos, Peter Montgomery
related to Derivation of the algorithm · 2
Lanczos algorithm → Lanczos, There
is a · 1
Lanczos algorithm → iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the m

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Important terminology

displaystyle lanczos algorithm vector eigenvalues matrix method vectors one since also power iteration eigenvalue eigenvectors dotsc may norm lambda real

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Lanczos algorithmis aiterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the m0.90text
restarted Lanczos bidiagonalizationinstance ofThis has led into a number of other restarted variations0.80text
the HITS algorithm developed by Jon Kleinberginstance ofEigenvectors are also important for large-scale ranking methods0.80text
or the PageRank algorithm used by Google.Lanczos algorithms are also used in condensed matter physics as a method for solving Hamiltonians of strongly correlated electron systemsinstance ofEigenvectors are also important for large-scale ranking methods0.80text
as well as in shell model codes in nuclear physicsinstance ofEigenvectors are also important for large-scale ranking methods0.80text
Lanczos algorithmhas applicationLanczos0.60section
Lanczos algorithmhas applicationSince0.60section
Lanczos algorithmhas applicationEigenvectors0.60section
Lanczos algorithmhas applicationHITS0.60section
Lanczos algorithmhas applicationJon Kleinberg0.60section
Lanczos algorithmhas applicationPageRank0.60section
Lanczos algorithmhas applicationGoogle0.60section

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