Matrix Algorithms, Volume II: Eigensystems

By G. Stewart. 2001

447 citations recorded by the source corpus.

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Explicit Time-Domain Finite-Element Method Stabilized for an Arbitrarily Large Time Step (2012, background): “is symmetric positive definite and being symmetric, the eigenvectors of (5) are -and -orthogonal [25].”
Unsupervised feature selection for multi-cluster data (2010, background): “(1) within O ( KNp ) time [27].”
SRDA: An Efficient Algorithm for Large-Scale Discriminant Analysis (2008, methodology): “When m ≥ n, the calculation of X̄X̄ requires 1 2mn 2 flam; Computing the eigenvectors of X̄X̄ requires 92n 3 flam [22], [12]; Recovering V from U requires mn(2) flam by assuming r is close to min(m,n); Computing the c eigenvectors of HH requires 12nc (2)+ 92c (3)+nc(2) flam; Finally, calculating a’s”
Spectral Regression for Efficient Regularized Subspace Learning (2007, methodology): “The most efficient algorithm to calculate the SVD decomposition requires 32m (2)n + 92m 3 flam [20].”
Randomized numerical linear algebra: Foundations and algorithms (2020, methodology): “For a comprehensive treatment of matrix computations, we refer to (Golub and Van Loan 2013, Trefethen and Bau III 1997, Stewart 1998, Stewart 2001).”
Spectral regression: a unified subspace learning framework for content-based image retrieval (2007, methodology): “The Lanczos algorithm can be used to iteratively compute the first d eigenvectors within dp1m(k + 8) flam, where p1 is the number of iterations3 in Lanczos [24].”