Albert T. Galick. Efficient solution of large sparse eigenvalue problems in microelectronic simulation. PhD thesis, University of Illinois at Urbana-Champaign, 1993. Home/Search Document Details and Download
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Inexact Newton Preconditioning Techniques for Eigenvalue.. - Wu, Saad, Stathopoulos (1998) (1 citation) (Correct)
....7 8 9 10 2 10 4 10 6 10 8 10 10 10 12 10 14 10 16 10 18 10 20 iteration condition number Figure 1: Condition numbers of the Jacobian matrices used by different Newton recurrences. The same iteration matrix J I has been used before in a so called Inflated Inverse Iterations [17]. Thus we refer to the recurrence formed from Equations (15) and (8) as the Inflated Newton Recurrence. This recurrence is well defined since it is always possible to choose an ff to make J I non singular. It is also easy to verify that the eigenpairs are the stationary points of the recurrence. ....
Albert T. Galick. Efficient solution of large sparse eigenvalue problems in microelectronic simulation. PhD thesis, University of Illinois at Urbana-Champaign, 1993.
Preconditioned Techniques For Large Eigenvalue Problems - Wu (1997) (5 citations) (Correct)
....Due to this unique construction, it avoids some of the pitfalls of the original Davidson preconditioning scheme. There are a number of eigenvalue methods that are based on Newton method for eigenvalue problems, for example, the trace minimization method [122] and the inflated inverse iteration [47]. Since we are interested in mimic the original Davidson preconditioning scheme, we will not directly adopt these methods as preconditioners though the idea may deserve some attention. In this section we will revisit the augmented Newton scheme proposed in [98] It is slightly reformulated so that ....
....EX2. The results is shown in table 3.2. Note that in this case, RQI converges to an eigenvalue within the large cluster around zero. 3.2. 2 Augmented Newton method One way of formulating the eigenvalue problem is to express it as finding a zero residual with ( x) pair as the independent variable [47, 89, 98]. This formulation can be described as seeking a solution to the following quadratic equation ae (A Gamma I)x = 0; Gamma 1 2 x T x 1 2 = 0: 3.10) The original form of this Newton method is presented in [98] Many researchers have noticed the scaling scheme in this paper was not ....
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Albert T. Galick. Efficient solution of large sparse eigenvalue problems in microelectronic simulation. PhD thesis, University of Illinois at Urbana-Champaign, 1993.
Inexact Newton Preconditioning Techniques for Eigenvalue.. - Wu, Saad, Stathopoulos (1998) (1 citation) (Correct)
.... I) Gamma1 1 ffx T i (A Gamma i I) Gamma1 x i : we can define yet another recurrence which computes ffi x as follows, ffi x = J Gamma1 I r i ; J I = A Gamma i I ffx i x T i : 15) The same iteration matrix J I has been used before in a so called Inflated Inverse Iterations [17]. Thus we refer to the recurrence formed from Equations (15) and (8) as the Inflated i i kr i k i 1 90685.22644 911704.3057 762 2 2500.224244 34828.83139 2.567e 04 3 0.2118515633 672.661174 2.807e 05 4 0.2109448763 0.01285108116 1.165e 12 5 0.2106508532 0.001874830432 2.23e 12 6 0.2097380827 ....
Albert T. Galick. Efficient solution of large sparse eigenvalue problems in microelectronic simulation. PhD thesis, University of Illinois at Urbana-Champaign, 1993.
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