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Spurious eigenvalues

The Cullum-Willoughby test,27,37 on the other hand, was designed to identify the so-called spurious eigenvalues, rather than the converged eigenvalues. In particular, the tridiagonal matrix T and its submatrix, obtained... [Pg.298]

This completes the definition of the stability problem for the mixed convection flow over the horizontal plate. For a given K and Re, one would be required to solve (6.4.19)-(6.4.38), starting with the initial conditions (6.4.39)-(6.4.58) and satisfy (6.4.63) for particular combinations of the eigenvalues obtained as the complex k and u>. We will use the procedure adopted in Sengupta et al. (1994) to obtain the eigen-spectrum for the mixed convection case, when the problem is in spatial analysis framework. In the process, it is possible to scan for all the eigenvalues in a limited part of the complex k- plane, without any problem of spurious eigenvalues. [Pg.209]

The kinetic energy operator corresponding to G z) is hermitian above. Loss of hermiticity may lead to spurious eigenvalues appearing in the calculations[42]. To avoid this, a proper basis should be chosen. For instance, to treat the term involving G z) in the RCL Hamiltonian, a Fourier D R basis was uscd[38]. [Pg.260]

The remarkable fact, first demonstrated by Nakatsuji [18], is that for each p >2, CSE(p) is equivalent (in a necessary and sufficient sense) to the original Hilbert-space eigenvalue equation, Eq. (2), provided that CSE(p) is solved subject to boundary conditions (A -representability conditions) appropriate for the (p + 2)-RDM. CSE(p), in other words, is a closed equation for the (p+ 2)-RDM (which determines the (p + 1)- and p-RDMs by partial trace) and has a unique A -representable solution Dp+2 for each electronic state, including excited states. Without A -representability constraints, however, this equation has many spurious solutions [48, 49]. CSE(2) is the most tractable reduced equation that is still equivalent to the original Hilbert-space equation, and ultimately it is CSE(2) that we wish to solve. Importantly, we do not wish to solve CSE(2) for... [Pg.265]

Now we easily see the origin of the spurious singularities that plague the FW approach. Let be an eigenfunction of Hq with eigenvalue Then... [Pg.726]

The possible severity of the problem has been shown by M. Stanke and J. Karwowski, Variationalprinciples in the Dirac theory Spurious solutions, unexpected extrema and other traps in A eir Trends in Quantum Systems in Chemistry and Physics, vol. I, pp. 175 190, eds. J. Maniani et al., Kluwer Academic Publishers, Dordrecht (2001). Sometimes an eigenfunction corresponds to a quite different eigenvalue. Nothing of that sort appears in non-relativistic calculations. [Pg.131]


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See also in sourсe #XX -- [ Pg.323 ]




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Eigenvalue

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