### Table 5.5: Comparisons of unsorted logic solutions of the streamroller problem in [Stickel, 1986, pp 93{94] with a natural deduction solution in SNIP 2.2

1993

Cited by 3

### Table 19. Natural frequencies obtained through dynamic excitation and solution of matrix eigenvalue problem (4.14).

"... In PAGE 58: ... It can be seen from the plots that the simulated voltage spike with small duration evoked the expected high frequency responses. The excited natural frequencies are compared in Table19 with those for the undamped shell which were obtained by solving the matrix eigenvalue problem... ..."

Cited by 1

### Table 13. Natural frequencies obtained through dynamic excitation and solution of the matrix eigenvalue problem (4.13).

"... In PAGE 32: ... Note that all computations were performed with double precision accuracy. In Table13 , the natural frequencies obtained through this dynamic patch excitation are compared with those obtained for the undamped shell by solving the matrix eigenvalue prob- lem (4.13).... ..."

### Table 2 First 10 open and closed loop eigenvalues for n = 100. 6. Summary. The well known orthogonality relations for the eigen- vectors of a symmetric matrix or a symmetric de nite pair are generalized to the triplet that de nes a symmetric de nite quadratic pencil. One of the three orthogonality relations for the quadratic pencil is then used to derive an explicit solution to the partial pole assignment problem for a second order system. The explicit solution is a powerful tool in the analysis of eigenvalue assignment problems and it lends itself naturally to the solution of the problem of stabilization and control of exible, large, space structures where only a small part of the spectrum is to be assigned and the rest of the spectrum is required to remain unchanged. The orthogonality relations may also be useful in investigating eigenvalue November 2, 1995, 18:35. Page: 15

1997

Cited by 17

### Table 2: Some formalisms used to specify structured dynamical systems according to the continuous or discrete nature of space, time, and state variables of the components. The heading Numerical Solutions refers to explicit numerical solutions of partial differential equations and systems of coupled ordinary differential equations.

2002

Cited by 1

### Table 3. We conclude this section with a description of a method which uses the MMPDEs to generate an initial equidistribution mesh. To be speci c, we only discuss it for the solution u(x; 0) in (75) with c(0) = 103. Since u(x; 0) is quite steep at x = 0:4, it is natural to employ a (pseudo-)time integration of the MMPDE to steady state with the resulting solution being the equidistribution mesh for u(x; 0). For illustration, we let

1994

Cited by 29

### Table 1: Solution time for an anisotropic problem with two orderings. Solution Ordering

1995

"... In PAGE 3: ... A zero initial guess was used, and the matrix was solved to a reduction of 10?12 in the l2 norm of the residual. Table1 shows the solution time when the matrix was ordered in two ways: natural x-y ordering numbered the nodes in the x direction rst, and natural y-x ordering numbered the nodes in the y direction rst. Theorem 1 will show why the incomplete factorization in the x-y direction was poorer, despite both preconditioners having the same level of ll, and... ..."

Cited by 16