T. Ericsson, Implementation and applications of the spectral transformation Lanczos algorithm, in Matrix Pencils, B. Kagstrom and A. Ruhe, eds., Berlin, 1983, Springer, pp. 177-188. (Lecture Notes in Mathematics, 973). Home/Search Document Not in Database Summary Related Articles Check |
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A Comparison Of Numerical Implementations Of The.. - Arbenz.. (2000) (Correct)
....respectively. Notice that in the QR algorithm the complete spectrum is computed When computing a few of the lowest eigenvalues of a sparse matrix eigenvalue problem A n x = x; A n = A T n ; 3. 1) it is advantageous to apply a spectral transformation to get a reasonable speed of convergence [21, 8, 19, 12]. In the shift and invert approach (3.1) is transformed into (A n I) 1 x = x; 1 : 3.2) The spectral transformation leaves the eigenvectors unchanged. The eigenvalues of (3.1) close to become the largest absolute of (3.2) In addition they are relatively wellseparated which improves ....
T. Ericsson, Implementation and applications of the spectral transformation Lanczos algorithm, in Matrix Pencils, B. Kagstrom and A. Ruhe, eds., Berlin, 1983, Springer, pp. 177-188. (Lecture Notes in Mathematics, 973).
Eigenvalue Solvers for Electromagnetic Fields in Cavities - Adam, Arbenz, Geus (1997) (2 citations) (Correct)
....eigenvalue problem Ax = Mx; A = A T ; M = M T 0; 7.1) simultaneously. If the desired eigenvalues are the ones closest to a number it is advisable to make a so called shift and invert approach and apply a spectral transformation with a shift oe close to and instead of (7. 1) solve [50] [20] [24] A Gamma oeM) Gamma1 Mx = x; 1 Gamma oe : 7.2) Notice that (A GammaoeM ) Gamma1 M is M symmetric, i.e. it is symmetric with respect to the inner product Initialization: Choose Q 0 2 R n Thetaq with Q 0 T MQ 0 = I q . i) Factor A Gamma oeM = LAL T A . Cholesky ....
T. Ericsson, Implementation and applications of the spectral transformation Lanczos algorithm, Matrix Pencils (Berlin) (B. Kagstršom and A. Ruhe, eds.), Springer, 1983, (Lecture Notes in Mathematics, 973), pp. 177--188.
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