A. Edelman. SIAM J. Matrix Anal. Appl., 9:543, 1988. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Numerical Methods for the QCD Overlap Operator: I. . . . - van den Eshof, Frommer.. (2002) (1 citation) (Correct)
....are bounded for this method. Krylov subspace methods for linear systems that are based on a Galerkin condition, like CG, often show a similar convergence behavior for inde nite problems. In this situation the peaks in the convergence history can cause instabilities in the linear solver, see e.g. [37,38]. For the Lanczos approximations (13) and (14) of the sign function this poses no serious problem if the case of zero Ritz values is properly handled. It only requires that we skip the result for one iteration. It can be shown that a Ritz value close to zero in two consecutive iterations implies ....
A. Greenbaum, SIAM J. Matrix Anal. Appl. 18 (1997) 535.
Recent Developments in Dense Numerical Linear Algebra - Higham (2000) (Correct)
....elements occurring during the elimination on A 2 IR . The long standing conjecture that ae n n for complete pivoting is now known to be false. Gould [70] found a counterexample in floating point arithmetic and Edelman modified it to create a counterexample in exact arithmetic [57] [58]. By how much ae n can exceed n for complete pivoting is not known. Examples that can occur in practical applications where partial pivoting yields exponentially large growth factors are identified by Foster [64] and Wright [131] while Higham and Higham [86] identify matrices for which any ....
Editor's note. SIAM J. Matrix Anal. Appl., 12(3), 1991.
Numerical Methods for the QCD Overlap Operator: I. .. - van den Eshof.. (2002) (1 citation) (Correct)
....are bounded for this method. Krylov subspace methods for linear systems that are based on a Galerkin condition, like CG, often show a similar convergence behavior for indefinite problems. In this situation the peaks in the convergence history can cause instabilities in the linear solver, see e.g. [37,38]. For the Lanczos approximations (13) and (14) of the sign function this poses no serious problem if the case of zero Ritz values is properly handled. It only requires that we skip the result for one iteration. It can be shown that a Ritz value close to zero in two consecutive iterations implies ....
A. Greenbaum, SIAM J. Matrix Anal. Appl. 18 (1997) 535.
Using Properties Of Random Matrices For Target Factor.. - Marth, Maier.. (Correct)
.... Pillai and Chang [18] obtained an approximation to the probability function in the region P 0:9. Sugiyama [19] has himself given an approximation in terms of 2 distributions useful for small =M Gamma K 5. If N and M are larger than 10 2 the use of asymptotic results (see e.g. [20]) is possible since the probability function tends to the unit step function. ffl Tables If standard values for ff are used there are tabulated values for P available. See e.g. 18] 21] This approach is especially versatile for embedded sensor systems that do not have extensive computing ....
A. Edelman, SIAM J. Matrix Anal. Appl., 9, 543 (1988).
New Tests Of Random Numbers For Simulations In Physical Systems - Vattulainen (1994) (2 citations) (Correct)
....method for studies of pseudorandom number generators is by means of random matrices. We have constructed one test of this kind, concentrating on distributions of condition numbers in Gaussian distributed random matrices. This condition number test is based on the theoretical work of Edelman [41]. Consider a real m Theta 2 matrix B with elements from a standard normal (Gaussian) distribution. We define a Wishart matrix W = BB T , and calculate its eigenvalues max and min ( max min 0) and the 2 norm condition number = q max = min of B. The probability distribution function ....
....B with elements from a standard normal (Gaussian) distribution. We define a Wishart matrix W = BB T , and calculate its eigenvalues max and min ( max min 0) and the 2 norm condition number = q max = min of B. The probability distribution function of for such a Gaussian matrix is [41] f( m Gamma 1)2 m Gamma1 2 Gamma 1 ( 2 1) m m Gamma2 ; 31) and its cumulative distribution function (cdf) is given by F (b) Z b 1 f( d (32) 1 Gamma 2b 1 b 2 m Gamma1 ; b 1: In the condition number test we proceed as follows. First, by using a pseudorandom ....
A. Edelman, SIAM J. Matrix Anal. Appl. 9, 543 (1988).
LA Numerical Linear Algebra - Copyright By (Correct)
.... with its root at vertex n (otherwise it is more accurately termed an elimination forest) The elimination tree, which we denote by T (A) is a spanning tree for the filled graph F (A) The many uses of the elimination tree in analyzing and organizing sparse Cholesky factorization are surveyed in [57]. We will illustrate these concepts pictorially in several examples below. 8.3 Sparse Factorization There are three basic types of algorithms for Cholesky factorization, depending on which of the three indices is placed in the outer loop: 1) Row Cholesky: Taking i in the outer loop, successive ....
J. Liu, SIAM J. Matrix Anal. Appl. 11, 134 (1990).
Limiting Form of the Sample Covariance Eigenspectrum in PCA.. - Hoyle, Rattray (2003) (Correct)
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A. Edelman. SIAM J. Matrix Anal. Appl., 9:543, 1988.
A Matlab Implementation of the Implicitly Restarted Arnoldi Method .. - Radke (1996) (5 citations) (Correct)
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SIAM J. Matrix Anal. Appl., 14#1#:45#58, 1993.
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Fausett, D. W., Fulton, C. T., 1994, SIAM J. Matrix Anal. Appl. 15, 219. 135
Geometric Filtering for Subspace Tracking - Srivastava, Klassen (2000) (2 citations) (Correct)
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SIAM Jour. Matrix Anal. Appl., 9#2#, April 1988.
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