Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices

Arnoldi, 1951, The principle of minimized iterations in the solution of the matrix eigenvalue problem, 9, 17

Björck, 1979, Accelerated projection methods for computing pseudo inverse solutions of systems of linear equations, Nordisk Tidskr. Informationsbehandling (BIT), 19, 145

Daniel, 1976, Reothogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comp., 30, 772

Golub, 1977, The block Lanczos method for computing eigenvalues, III, 361

Jennings, 1975, Simultaneous iteration for partial eigensolution of real matrices, J. Inst. Math. Appl., 15, 351, 10.1093/imamat/15.3.351

Kaniel, 1966, Estimates for some computational techniques in linear algebra, Math. Comp., 20, 369, 10.1090/S0025-5718-1966-0234618-4

Krasnoselskii, 1972

Lanczos, 1950, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards, 45, 255, 10.6028/jres.045.026

Lewis, 1977, Algorithms for sparse matrix eigenvalue problems, Ph.D. Thesis

Lorentz, 1966

Paige, 1971, The computation of eigenvalues and eigenvectors of very large sparse matrices

Paige, 1974, Bidiagonalization of matrices and solution of linear equations, SIAM J. Numer. Anal., 11, 197, 10.1137/0711019

Parlett, 1980

Ruhe, 1979, Implementation aspects of band Lanczos algorithms for computation of eigenvalues of large sparse matrices, Math. Comp., 33, 680, 10.1090/S0025-5718-1979-0521282-9

Saad, 1974, Calcul de valeurs propres de grandes matrices hermitiennes par des techniques de partitionnement

Y. Saad, On the rates of convergence of the Lanczos and the block Lanczos methods, SIAM J. Numer. Anal., to appear.

Saad, 1979, Etude de la convergence du procédé d'Arnoldi pour le calcul d'éléments propres de grandes matrices non symetriques, 321

Stewart, 1973

G.W. Stewart, SRRIT, a FORTRAN subroutine to calculate the dominant invariant subspace of a real matrix, ACM Trans. Math. Software, to appear.

Wilkinson, 1965