Tutor: WangZhengSheng

School: Nanjing University of Aeronautics and Astronautics

Course: Computational Mathematics

Keywords: nonlinear eigenvalue problem shift-and-invert Arnoldi cubic eigenvalue problem Jacobi-Davidson method linearlization

CLC: O241.6

Type: Master's thesis

Year: 2010

Downloads: 26

Quote: 0

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Solving nonlinear eigenvalue problems is a hot spot of computational mathematics and science and engineering field. polynomial eigenvalue problems (PEP for short), especially quadratic eigenvalue problem(QEP) and cubic eigenvalue problem(CEP), is a typical nonlinear eigenvalue problems. Most of them are arising in the dynamic analysis of structural mechanical, and acoustic systems, in electrical circuit simulation, in fluid mechanics, and, more recently, in modeling microelectronic mechanical systems and so on.For solving the large scale cubic eigenvalue problem(CEP) L (λ) x = (λ~ 3 A +λ~ 2B +λC + D ) x= 0, First of all, the thesis introduced iterated shift-and-invert Arnoldi algorithm. This algorithm, which is a direct projection method combined with the shift-and-invert technique in Arnoldi Process, has the virtues of higher computational efficiency and rapid convergence. The thesis also studied Jacobi-Davidson method for polynomial eigenvalue problems. Took Quadratic Eigenvalue Problem (QEP for short) for example, the thesis studied linearlization Jacobi-Davidson method and direct Jacobi-Davidson method, and did a comparative analysis. Finally, wrote programs to achieve the above algorithms, then did numerical experimentations and compared the results. Numerical examples given in this thesis confirmed new method’s effectiveness and advantage compared to the existing clipping algorithm. |

- The Improved Block Jacobi-Davidson Method for Solving Large Symmetric Eigenvalue Problems,O241.6
- Block Jacobi-Davidson Method for Solving Generalized Symmetirc Eigenvalue Problems,O241.6
- A Class of Iterative Projection Methods for Nonlinear Large Sparse Eigenvalue Problems,O241.6
- Fourth-order Two Boundary Value Problems,O302
- Nonlinear Eigenvalue Problems with Low-Rank Damping: Theories and Algorithms,O241.6
- Parallel Computation of Eigenvalue Problems,O302
- Block Jacobi-Davidson Method for Large Eigenproblems,O241.6
- Refined Jacobi-Davidson Type Method for a Right Definite Two-Parameter Eigenvalue Problem,O241.6
- The Study of a Radial Point Interpolation Meshless Method with Polynomial Basis and It’s Application,O241
- The Semilocal Convergence Properties of Super-Halley Method and Newton Method under Weak Conditions,O241.7
- Three-dimensional unsteady heat conduction boundary element method and numerical systems development,O241.82
- A Jump Condition Capturing Scheme for Elliptic Interface Problems,O241.82
- Spectral Method for Solving Two Types of Delay Differential Equations,O241.8
- Research on Parallel Jacobi Method for SVD Problem,O241
- High Order Finite Difference Schemes for Convection-Diffusion Equation,O241.82
- Stability analysis of Pantograph Equations,O241.8
- Research on Some Problems of Moving Least Square Method in the Data Fitting,O241.5
- The High Accurate and Conservative Numerical Scheme for a Coupled Nonlinear Schr(?)dinger Ssytem,O241.82
- Further Study on the Error Estimates for Least Squares Problems,O241.5
- The Method of Characteristic Block Centered Difference for Regularised Long Wave Equation,O241.82
- The Lumped Mass Finite Element Method for Second Order Hyperbolic Equtions,O241.82
- Study of numerical methods for Volterra integral equations of the first kind,O241.83

CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Linear algebra method of calculating

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