The Lanczos algorithm is an iterative method devised by Cornelius Lanczos. It is an adaptation of power methods to find the most useful eigenvalues and eigenvectors of a Hermitian matrix, meaning a limited number of them, often much smaller than the size of the matrix. The lead notes that although the method is computationally efficient in principle, it was not useful as initially formulated because of its numerical instability. It therefore stands as an example of a numerical linear algebra procedure whose practical value depended on later understanding of how rounding errors behave.
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Lanczos algorithm (Wikipedia)
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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
In Field: Algorithms and Complexity Theory, Lead
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 than n {\displaystyle n} .
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