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Computational techniques

ELPA - Eigenvalue Solvers for Petaflop Applications

LAPACK Users' Guide

ARPACK - Implicitly Restarted Arnoldi Method

JADAMILU - computing selected eigenvalues of large sparse symmetric matrices

Expokit - computing small dense and large sparse matrix exponentials in FORTRAN and MATLAB

Matrix market - Test data for comparative studies of algorithms for numerical linear algebra (NIST)


Arnoldi iteration (Wikipedia)

Lanczos algorithm (Wikipedia)


Y Saad, Numerical methods for large eigenvalue problems (SIAM, 2011), rev 2ed

Weibe A, Wellein G, Alvermann A, Fehske H, The kernel polynomial method, RMP 78, 275 (2006)

Y Saad, Iterative methods for sparse linear systems (SIAM, 2003), 2ed

C Moler, C Van Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev 45, 3 (2003)

D Watkins, Fundamentals of matrix computations (Wiley, 2002), 2ed

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Numerical analysis 2000. Vol.3. Linear algebra, J Comput Appl Math 123 (2000)

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Икрамов Х Д, Несимметричная проблема собственных значений. Численные методы (Наука, 1991)

Парлетт Б, Симметричная проблема собственных значений. Численные методы (Мир, 1983)

Фаддеев Д К, Фаддеева В Н, Вычислительные методы линейной алгебры (М-Л, 1963), 2изд


A Maillard, F Krzakala, M Mezard, L Zdeborova, Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising, JSM 2022, 083301 (2022)

Iitaka T, Ebisuzaki T, Random phase vector for calculating the trace of a large matrix, PRE 69, 057701 (2004)

Jie Q, Liu D, Modified conjugate gradient method for diagonalizing large matrices, PRE 68, 056706 (2003)

Andreozzi F, Porrino A, Iudice N Lo, A simple iterative algorithm for generating selected eigenspaces of large matrices, JPA 35, L61 (2002)

Tackett A R, Ventra M Di, Targeting specific eigenvectors and eigenvalues of a given Hamiltonian using arbitrary selection criteria, PRB 66, 245104 (2002)