1. The difficult problems associated with adjacent or confluent eigenvalues are outlined and methods of solution developed and discussed.

2. Having obtained the eigenvalues, can readily find the corresponding eigenvectors.

3. However, complex eigenvalues and vectors are of frequent occurrence, and require special consideration.

4. This notion of eigenvalues gives numbers a natural lodgement in the theory of operators acting on vector spaces.

5. Approximation solution of the algebraic eigenvalue problem.

6. A class of eigenvalue problems is studied.

7. Parallel computation for the nonsymmetric generalized eigenvalue problem is one of the fundamental problems in large scale engineering computation.

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8. Distill the eigenvalue of the magnetic leakage to the second BP data fusion network to judge the length, width, depth.

9. And then the eigenvalue problem of integral equation is transformed into the standard eigenvalue problem of a positive definite matrix with infinite order.

10. The derivation of eigenvalue problem for characteristic wave number is carried out based on Maxwell equations.

11. Based on mean theorem, the method combines Jacobian's eigenvalue with its eigenvector to form a null space vector of redundant robot.

12. Introduces the two - eigenvalue problem of a symmetric matrix and gives a formula to compute the matrix.

13. Subspace method is an efficient tool for generalized eigenvalue problem in scientific and engineering computing.

14. The eigenvalue problem of radially inhomogeneous cylindrical dielectric waveguides is solved by microwave network method.

15. Although some people have solved the eigenstate and eigenvalue with periodic boundary condition , the open boundary condition has not been given out yet .

16. In this paper, the eigenvalue problems of multilayer dielectric waveguide consisting of arbitrary number of layers are solved by microwave network method.

17. The real numbers which result from making measurements are interpreted as the eigenvalues of the corresponding observable.

18. The chapter ends with an extensive discussion of Kron's eigenvalue method followed by proofs of the Wittrick-Williams and Simpson counting algorithms.

19. Advantageous as that is in its proper place it would be disastrous if such numbers turned up as eigenvalues.

20. Methods The upper-lower solutions, monotone derivative methods, the maximum principle, comparison principle and principal eigenvalue theory were used.

21. Through changing some parameters such as type, frequency, amplitude, offset, and so on, it can get the amplitude eigenvalue that corresponding with the cycle signal and the stochastic signal.

22. The boundary element method is applied to solve the three dimensional boundary value problem. The differential equations are transformed to a generalized eigenvalue problem to be solved.

23. After the equation is set up, using the standard finite element program and subspace iteration algorithm to solve the generalized eigenvalue problem.

24. In this paper we introduce mainly our work on parallel processing for nonsymmetric matrix generalized eigenvalue problem.

25. A novel DOA estimation algorithm based on the largest eigenvalue of the covariance matrix is presented. It mainly applies to the pencil beam smart antenna in DS CDMA systems.

26. As applications of majorizing inequality of convex function of several variables, some majorizing inequalities of eigenvalue and singular value of matrix are obtained.

27. To this end we shall first consider the following eigenvalue problem.

28. It is found that the synchronization time of N linear SDE is determined by the second maximum eigenvalue of interaction matrix.

29. Then stability of the system depends on the corresponding second - order eigenvalue problem.

30. In this paper , We obtain the new bounds for the greatest eigenvalue of a nonnegative matrix.

31. The eigenvalue of covariance matrix can be used to separate signal from noise.

32. Discreteness of eigenvalue spectra for a class of eigenvalue problems is proved through integral equation representation.

33. Finally, the problem is converted to the generalized eigenvalue problem, so that the maximum proportional gain can be optimized.

34. When the minimal eigenvalue of connection weights matrix is greater than the reciprocal of derivation of its neuron activation function, the network will be convergent in parallel update mode.

35. An initial quantity parameter(QP) prejudgment(IQPP) algorithm that can predict the initial QP precisely is proposed based on statistics of encoded frames and frame complexity eigenvalue of I frame.

36. From this character, the relationship betweethe symmetric and the antisymmetric eigenvalue problem can be found, which reflects the inherent property of the corresponding problem.

37. Section four, We give the estimate of Dirac - Laplacian operator's eigenvalue gap on some restricted conditions.

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38. We construct a generalized eigenvalue problem based on orthogonal least square technique.

39. The Solutions of eigenvalue and eigenfunction for three non - self - adjoint situation are summarized.

40. When generalized eigenvalue problem is solved with the aid of a simultaneous iteration algorithm, the initial test vector may be automatically generated by means of random numbers.

41. Afterwards, the inverse quadratic eigenvalue problems in damped vibration system are studied.

42. Additional inter-area damping control (AIADC) is proposed for generators' excitation controllers, and the effect of delayed feedback signal is demonstrated by using eigenvalue analysis.

43. It is discussed that the methods of discrimination of the stability of the singular point of nonlinear autonomous system by using of eigenvalue, center manifold and Liapunov function.

44. This paper mainly discusses the formulation and the numerical methods of real symmetrical matrix inverse algebraic eigenvalue.

45. This paper presented spatial relation descriptor based on metric matrix's eigenvalue which was invariant under translation, scaling and rotation.

46. Parallel processing for generalized eigenvalue problem is one of the fundamental problem in computation science and engineering.

47. Formerly the FEM perturbation method is to make the same small varieties of mass matrix and stiffness matrix, then calculate changes of system's eigenvalue and eigen vector.

48. The paper proposes the using of modal interval theory in solving the generalized eigenvalue of interval equations, discuss the using of MIA theory in matrix operation.

49. Introduces the two - eigenvalue problem of a symmetric matrix and gives a formula to compute matrix.

50. In this paper, we use the method of the estimated characteristic function to estimate a lower bound of the first eigenvalue on compact Riemann manifold.

51. In order to research the buckling process of three-dimensional trusses, the eigenvalue buckling analysis and non-linear flection analysis are carried out.

52. This paper discusses the structure, calculation of multiplication and power, eigenvalue and eigenvector, and diagonalizable problems of matrix of rank equal to 1.

53. As far as the second eigenvalue problem was concerned, the expansion theorem was proved by the theory of completely continuous operator (compact operator).

54. The chain coding is built by eigenvalue of region description that is partite from image. The grid feature couple is used to locate and detect the human face for the captured image.

55. Eigenvalue method is one of the fundamental Methods: That solve polynomial system.

56. We can not say for certain which eigenvalue will be obtained.

57. It is shown that the eigenvalue distribution is a function of these multipath parameters.

58. The eigenfunction and eigenvalue of the equation are solved by the non-degenerate perturbation theory, as well as dispersion relations for the spin wave.

59. An eigenvalue - based objective function to increase the system damping is proposed.

60. Under distribution , each eigenvalue can be described by its mean and variance.

61. Where EVM is the sum of eigenvalue of bonding orbital-connection matrix of the alkyl group and PEI is the polarizibility of alkyl.

62. This paper employs the finite element method to solve the eigenvalue problem on the stability of a perturbed 2D magnetohydrodynamics (MHD) model of an aluminum reduction cell.

63. Matrix iteration method can be employed to figure out the first eigenvalue and eigenvector of a matrix.

64. Using homotopy methods, this paper gives an analysis on the existence of zeros of the decomposable mapping, and finds its application to a class of nonlinear eigenvalue problems.

65. We researched the subspace eigenvalue decomposition and weighted subspace fitting techniques in the beam space.

66. Then the eigenvalue problem of free vibration of annular sector plates is transformed into the eigenvalue problem of integral equation by using superposition theorem.

67. The structural performances are evaluated from the condition number (CN) of equilibrium matrix(sentence dictionary), and CN and minimum eigenvalue of stiffness matrix.

68. As for the perfect controllable system, the necessary condition satisfied by the eigenvalue of the state matrix A is now given.

69. An iteration procedure can be used to determine the eigenvalue.

70. Some applications of this method in the eigenvalue problems are demon - strated.

71. An inverse eigenvalue problem for damped gyroscopic systems is considered.

72. We build a set of complete bases through resolving the eigenvalue problem of this linear operator and prove its completeness and orthogonality.

73. It shows that the presented method can be used to identify modal parameters effectively under ambient excitation and that the polynomial eigenvalue method is superior to the augmented matrix method.

74. Finally, the numerical analysis was completed after the solution of generalized eigenvalue problem.

75. Based on complex torque coefficient method and eigenvalue analysis, the subsynchronous oscillation(SSO) damping characteristics of an AC/DC parallel system were studied.

76. The eigenvalue assignment problem is a classical problem in control systems.

77. Discuss the using of modal interval theory in solving the dynamic eigenvalue of uncertain parameters system. Research the divergence problem of solving interval and convergence rate problem.

78. Firstly, a perturbation and spaced eigenvalue problems of vibrating string is presented.

79. Massively Parallel Processing system (MPP) and PC cluster provide distributed-memory environments for parallel solving the generalized eigenvalue problem.

80. We construct the sparse eigenvalue by means of the sparsity of polynomial equations in this paper, and prove its equivalence theorem.

81. In this paper, the second equivalence theorem of eigenvalue method for solving sparse polynomial equations is proved.

82. Eddy current impedance diagram analysis method has high ability in classifying flaw Signals. Sig-nals are charactered by autocorrelation matrix eigenvalue and eigenvector of the signals measured.

83. The eigenvalue problem concerns two first-order ordinary differential equations and one second-order equation. Their coefficients depend on physics variables and gradients.

84. In this paper, we give a general spectral resolution of real matrix and some properties eigenvalue of a general positive definite real matrix.

85. The scalar is then called the eigenvalue associated with the eigenvector.

86. In this paper, we present an inverse eigenvalue problem for real bi - antisymmetric matrices.

87. New algorithm of matrix inverse iteration on the eigenvalue problem are presented in this paper.

88. A new method for human face image scale and direction estimation is proposed using covariance matrix eigenvalue and eigenvector of edge set, which is proved by theory and experiments.

89. The synchronization time in coupled N neurons (see chapter 4)The synchronization time of N linear SDE is determined by the second maximum eigenvalue of interaction matrix.

90. In this paper, we give the upper and lower bounds of the largest quasi-Laplace eigenvalue of a connected graph by algebraic method.

91. Done clinic experiments to validate the curative effect of OA-kneepad and the feasibility for energy of EMG as the eigenvalue, to evaluate the curative effect of KOA.

92. This paper indicated that the sequence of approximate value of eigenvalue is monotone convergent in the iteration process of matrix iteration method. And also gave examples.

93. By comparing the results for the linear function and cubic polynomial function and the convergences of eigenvalue.

94. In this paper, criteria for positive or negative real part of eigenvalue of matrix are given.

95. In this paper, firstly, eigenvalue equations of 2 D and 3 D in plane wave method are obtained.

96. Contraposirig the effect of materials capability, the conception of the characteristic equation and eigenvalue of relative cone radius are put forward.

97. A new test signal method based approach to design power oscillation damping (POD) controller for TCSC is proposed, by which the bulky eigenvalue calculation of state matrix can be avoided.

98. Like the deformation modulus, the electrical conductivity is such an eigenvalue that it will characterize well the damage of conductible concrete.

99. An inequality about degree of vertex of a connected graph can be given, and the upper bounds of the largest eigenvalue of the quasi-Laplacian matrix of a connected graph can be obtained.

100. In this paper, backward errors for seven kinds of structured unitary matrix eigenvalue problems are discussed.

101. Aiming at large cantilevered solid truss structure, the influence of purlin and the joints of web member and chord to structure displacement, eigenvalue buckling, nonlinear buckling were researched.

102. Based on model design and rotary wing design of helicopters, this paper introduces a multi targets inverse eigenvalue problem and gives a parallel method.

103. In this paper, We study the perturbation problem of eigenvalue of a simple graph G to adding and deleting an edge.

104. Recently, the interval analysis method has been used to deal with the static displacement and eigenvalue analysis of the uncertain structures with interval parameters.

105. Existence conditions of semi-trivial equilibrium solutions with principal eigenvalue theory of partial difference operator and comparison principle were analyzed.

106. One kind of inverse eigenvalue problems, whose solutions are required to be normal or diagonalizable matrices, is investigated in quaternionic quantum mechanics.

107. In this paper, we consider the best approximation of a matrix under a given linear restriction with some fixed elements. This result can be apply to solving a class matrix inverse eigenvalue problem.

108. The paper submit a indirect and universal method to solving variation problem in N-dimensional space, by way of transforming variation problem to eigenvalue problem of partial differential equation.

109. This paper studies inverse design problem of generalized eigenvalue problem of linear parameter discrete vibration system.

110. The sparse finite element is considered for solving eigenvalue problems. Based on an interpolation postprocessing, superconvergence estimates of both eigenfunction and eigenvalue are obtained.

111. An inverse eigenvalue produce for damage detection of rods is established.

112. The purpose of this paper is to find out an approach of inverse eigenvalue problems of undamped mass-spring system by using an attached lump of known mass.

113. The method derives from eigenvalue issue, regards Poison ratio and elastic modulus as a constant and a stochastic variable, respectively, and in terms of known data and a combination of the FEM.