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The ubiquitous Lanczos method can approximate $f(A)x$ for any symmetric $n \times n$ matrix $A$, vector $x$, and function $f$.
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
Cornelius Lanczos · 1950
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Methods of conjugate gradients for solving linear systems
Magnus R Hestenes and Eduard Stiefel · 1952
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A note on the summation of chebyshev series
C. W. Clenshaw · 1955
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Rounding Errors in Algebraic Processes
James H. Wilkinson · 1965
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The computation of eigenvalues and eigenvectors of very large sparse matrices
Christopher C. Paige · 1971
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Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix
Christopher C. Paige · 1976
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Rank-one modification of the symmetric eigenproblem
James R. Bunch, Christopher P. Nielsen, and Danny C. Sorensen · 1978
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The Lanczos algorithm with selective orthogonalization
Beresford N. Parlett and David S. Scott · 1979
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Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
Christopher C. Paige · 1980
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The Lanczos algorithm with partial reorthogonalization
Horst D. Simon · 1984
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On the rate of convergence of the preconditioned conjugate gradient method
Owe Axelsson and Gunhild Lindskog · 1986
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A fast algorithm for particle simulations
Leslie Greengard and Vladimir Rokhlin · 1987
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Behavior of slightly perturbed Lanczos and conjugate-gradient recurrences
Anne Greenbaum · 1989
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A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines
Michael F. Hutchinson · 1990
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Error bounds in the simple Lanczos procedure for computing functions of symmetric matrices and eigenvalues
Vladimir Druskin and Leonid Knizhnerman · 1991
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Analysis of some Krylov subspace approximations to the matrix exponential operator
Yousef Saad · 1992
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Estimates in quadratic formulas
Gene H. Golub and Zdeněk Strakoš · 1994
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Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic
Vladimir Druskin and Leonid Knizhnerman · 1995
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A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem
Ming Gu and Stanley C. Eisenstat · 1995
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Using nonorthogonal Lanczos vectors in the computation of matrix functions
Vladimir Druskin, Anne Greenbaum, and Leonid Knizhnerman · 1998
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The symmetric eigenvalue problem
Beresford N. Parlett · 1998
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Accuracy and stability of numerical algorithms
Nicholas J. Higham · 2002
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Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
Cleve Moler and Charles Van Loan · 2003
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Numerical Methods for Large Eigenvalue Problems: Revised Edition
Yousef Saad · 2011
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Approximating the exponential, the Lanczos method and an Õ(m)-time spectral algorithm for balanced separator
Lorenzo Orecchia, Sushant Sachdeva, and Nisheeth K. Vishnoi · 2012
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The noisy power method: A meta algorithm with applications
Moritz Hardt and Eric Price · 2014
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Faster algorithms via approximation theory
Sushant Sachdeva and Nisheeth K Vishnoi · 2014
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Large-scale log-determinant computation through stochastic Chebyshev expansions
Insu Han, Dmitry Malioutov, and Jinwoo Shin · 2015
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Randomized block Krylov methods for stronger and faster approximate singular value decomposition
Cameron Musco and Christopher Musco · 2015
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Iterative methods for sparse linear systems
Yousef Saad · 2003
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Sanjeev Arora, Elad Hazan, and Satyen Kale · 2005
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The Lanczos and conjugate gradient algorithms in finite precision arithmetic
Gérard Meurant and Zdeněk Strakoš · 2006
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A combinatorial, primal-dual approach to semidefinite programs
Sanjeev Arora and Satyen Kale · 2007
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Iteratively constructing preconditioners via the conjugate gradient method
John Dunagan and Nicholas J. A. Harvey · 2007
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Numerical Methods for Special Functions
A. Gil, J. Segura, and N. Temme · 2007
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