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Relevant bibliographies by topics / Eigenproblems

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Academic literature on the topic 'Eigenproblems'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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Journal articles on the topic "Eigenproblems"

1

Acho, Thomas M., and Dominic P. Clemence. "The parameter dependent Sturm-Liouville eigenproblem with an interior simple or double pole." ANZIAM Journal 43, no. 4 (2002): 479–91. http://dx.doi.org/10.1017/s1446181100012098.

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AbstractBoundary value problems where resonance phenomena are studied are most often transformable to parameter dependent Sturm-Liouville (SL) eigenproblems with interior singularities. The parameter dependent Sturm-Liouville eigenproblem with interior poles is examined. Asymptotic approximations to the solutions are obtained using an extended Langer's method to take care of the resulting complex eigenvalues and eigenfunctions.

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Ju, S. H., and H. H. Hsu. "An Out-of-Core Eigen-Solver with OpenMP Parallel Scheme for Large Spare Damped System." International Journal of Computational Methods 16, no. 07 (2019): 1950038. http://dx.doi.org/10.1142/s0219876219500385.

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An out-of-core block Lanczos method with the OpenMP parallel scheme was developed to solve large spare damped eigenproblems. The symmetric generalized eigenproblem is first solved using the block Lanczos method with the preconditioned conjugate gradient (PCG) method, and the condensed damped eigenproblem is then solved to obtain the complex eigenvalues. Since the PCG solvers and out-of-core schemes are used, a large-scale eigenproblem can be solved using minimal computer memory. The out-of-core arrays only need to be read once in each Lanczos iteration, so the proposed method requires little e

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Guillaume, Philippe. "Nonlinear Eigenproblems." SIAM Journal on Matrix Analysis and Applications 20, no. 3 (1999): 575–95. http://dx.doi.org/10.1137/s0895479897324172.

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Rivas, Mauricio A., and Stephen B. Robinson. "Eigencurves for linear elliptic equations." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 45. http://dx.doi.org/10.1051/cocv/2018039.

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This paper provides results forvariational eigencurvesassociated with self-adjoint linear elliptic boundary value problems. The elliptic problems are treated as a general two-parameter eigenproblem for a triple (a,b,m) of continuous symmetric bilinear forms on a real separable Hilbert spaceV.Geometric characterizationsof eigencurves associated with (a,b,m) are obtained and are based on their variational characterizations described here. Continuity, differentiability, as well as asymptotic, results for these eigencurves are proved. Finally, two-parameter Robin–Steklov eigenproblems are treated

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Muc, A., and A. Banaś. "Eigenproblems in nanomechanics." Bulletin of the Polish Academy of Sciences Technical Sciences 63, no. 3 (2015): 819–25. http://dx.doi.org/10.1515/bpasts-2015-0093.

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Abstract The paper is semitutorial in nature to make it accessible to readers from a broad range of disciplines. Our particular focus is on cataloging the known problems in nanomechanics as eigenproblems. Physical insights obtained from both analytical results and numerical simulations of various researchers (including our own) are also discussed. The paper is organized in two broad sections. In the second section the attention is focused on the analysis of quantum dots. The analysis of electronic properties of strained semiconductor structures is reduced here to the solution of a linear bound

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Sleijpen, Gerard L. G., Albert G. L. Booten, Diederik R. Fokkema, and Henk A. van der Vorst. "Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems." BIT Numerical Mathematics 36, no. 3 (1996): 595–633. http://dx.doi.org/10.1007/bf01731936.

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Bertolini, Adrian F. "Review of Eigensolution Procedures for Linear Dynamic Finite Element Analysis." Applied Mechanics Reviews 51, no. 2 (1998): 155–72. http://dx.doi.org/10.1115/1.3098994.

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This article reviews the solution procedures used to extract eigenvalues and eigenvectors from linear dynamic systems using the finite element method. The main focus of this review article is on eigensolution techniques that provide only a partial eigensolution. Such eigensolvers extract only a small subset (normally the lowest) of the eigenvalues and eigenvectors present in the discretized system. They represent the most efficient approach to extracting eigenvalues and eigenvectors from large degree of freedom systems. The techniques covered include the subspace iteration method, the Lanczos

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Benner, Peter, and Daniel Kressner. "Balancing sparse Hamiltonian eigenproblems." Linear Algebra and its Applications 415, no. 1 (2006): 3–19. http://dx.doi.org/10.1016/j.laa.2004.09.023.

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Gambolati, Giuseppe, Giorgio Pini, and Mario Putti. "Nested Iterations for Symmetric Eigenproblems." SIAM Journal on Scientific Computing 16, no. 1 (1995): 173–91. http://dx.doi.org/10.1137/0916012.

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Corless, Robert M. "Gröbner bases and matrix eigenproblems." ACM SIGSAM Bulletin 30, no. 4 (1996): 26–32. http://dx.doi.org/10.1145/242961.242968.

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Dissertations / Theses on the topic "Eigenproblems"

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Taslaman, Leo Viktor. "Algorithms and theory for polynomial eigenproblems." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/algorithms-and-theory-for-polynomial-eigenproblems(38fbb1cd-5144-4890-9979-b5e073014e5b).html.

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In this thesis we develop new theoretical and numerical results for matrix polynomials and polynomial eigenproblems. This includes the cases of standard and generalized eigenproblems. Two chapters concern quadratic eigenproblems $(M\lambda^2+D\lambda+K)x=0$, where $M$, $D$ and $K$ enjoy special properties that are commonly encountered in modal analysis. We discuss this application in some detail, in particular the mathematics behind discrete dampers. We show how the physical intuition of a damper that gets stronger and stronger can be mathematically proved using matrix analysis. We then develo

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Hao, Yujue. "Solving Eigenproblems with application in collapsible channel flows." Thesis, University of Glasgow, 2013. http://theses.gla.ac.uk/4589/.

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Collapsible channel flows have been attracting the interest of many researchers, because of the physiological applications in the cardiovascular system, the respiratory system and urinary system. The linear stability analysis of the collapsible channel flows in the Fluid-Beam Model can be finalized as a large sparse asymmetric generalized eigenvalue problem, where the stiffness matrix is sparse, asymmetric and nonsingular, and the mass matrix is sparse, asymmetric and singular. The dimensions of the both matrices can reach about ten thousand or more, and the traditional QZ Algorithm is so expe

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KURKA, PAULO ROBERTO GARDEL. "NUMERICAL SOLUTIONS FOR EIGENPROBLEMS ASSOCIATED TO SYMMETRIC OPERATORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1985. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=20274@1.

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Desenvolve-se uma técnica para a extração de auto-pares relacionados com a solução de problemas de Elementos Finitos. O algoritmo consiste no uso dos métodos da Iteração Inversa e Gradiente Conjugado para a obtenção do vetor solução associado ao menor auto-valor. As soluções do auto-sistema são calculadas sequencialmente pela modificação da matriz dos coeficientes das equações de equilíbrio do problema através do uso de uma técnica de Deflação. O uso extensivo desta técnica introduz auto-valores múltiplos na matriz dos coeficientes, tornando necessário proceder-se a uma combinação dos dois mét

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Maple, Carsten R. "A special numerical method for solving Hamiltonian eigenproblems." Thesis, University of Leicester, 1998. http://hdl.handle.net/2381/30540.

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In this thesis we develop and implement a new algorithm for finding the solutions of linear Hamiltonian systems arising from ordinary differential equation (ODE) eigenproblems; a large source of these systems is Sturm-Liouville problems, and these will provide the angle of approach. The convergence properties of the algorithm will be analysed, as will the performance of the algorithm for large values of eigenparameter. An algorithm is also proposed to find high-index eigenvalues of general Sturm-Liouville problems.

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Benner, Peter. "Structured Krylov Subspace Methods for Eigenproblems with Spectral Symmetries." Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000852.

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We consider large and sparse eigenproblems where the spectrum exhibits special symmetries. Here we focus on Hamiltonian symmetry, that is, the spectrum is symmetric with respect to the real and imaginary axes. After briefly discussing quadratic eigenproblems with Hamiltonian spectra we review structured Krylov subspace methods to aprroximate parts of the spectrum of Hamiltonian operators. We will discuss the optimization of the free parameters in the resulting symplectic Lanczos process in order to minimize the conditioning of the (non-orthonormal) Lanczos basis. The effects of our findings

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Carr, Arielle Katherine Grim. "Recycling Techniques for Sequences of Linear Systems and Eigenproblems." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/104143.

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Sequences of matrices arise in many applications in science and engineering. In this thesis we consider matrices that are closely related (or closely related in groups), and we take advantage of the small differences between them to efficiently solve sequences of linear systems and eigenproblems. Recycling techniques, such as recycling preconditioners or subspaces, are popular approaches for reducing computational cost. In this thesis, we introduce two novel approaches for recycling previously computed information for a subsequent system or eigenproblem, and demonstrate good results for seq

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Lampe, Jörg [Verfasser]. "Solving regularized total least squares problems based on Eigenproblems / von Jörg Lampe." Berlin : dissertation.de, 2010. http://d-nb.info/100768478X/34.

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Lamas, Daviña Alejandro. "Dense and sparse parallel linear algebra algorithms on graphics processing units." Doctoral thesis, Universitat Politècnica de València, 2018. http://hdl.handle.net/10251/112425.

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Una línea de desarrollo seguida en el campo de la supercomputación es el uso de procesadores de propósito específico para acelerar determinados tipos de cálculo. En esta tesis estudiamos el uso de tarjetas gráficas como aceleradores de la computación y lo aplicamos al ámbito del álgebra lineal. En particular trabajamos con la biblioteca SLEPc para resolver problemas de cálculo de autovalores en matrices de gran dimensión, y para aplicar funciones de matrices en los cálculos de aplicaciones científicas. SLEPc es una biblioteca paralela que se basa en el estándar MPI y está desarrollada con la p

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Wang, Diangin. "Solving the algebraic eigenproblem on parallel computers." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ31909.pdf.

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Willems, Paul. "On MR3-type Algorithms for the Tridiagonal Symmetric Eigenproblem and the Bidiagonal SVD." Wuppertal Universitätsbibliothek Wuppertal, 2010. http://d-nb.info/1002687853/34.

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Books on the topic "Eigenproblems"

1

Gilboa, Guy. Nonlinear Eigenproblems in Image Processing and Computer Vision. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75847-3.

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Gragg, William B. A divide and conquer method for unitary and orthogonal eigenproblems. Naval Postgraduate School, 1989.

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Ammar, Gregory S. Direct and inverse unitary eigenproblems in signal processing: An overview. Naval Postgraduate School, 1993.

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Johnston, Catherine M. Simultaneous iteration methods for the eigenproblem. The Author], 1992.

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5

Thurston, Gaylen A. A parallel solution for the symmetric eigenproblem. National Aeronautics and Space Administration, Langley Research Center, 1987.

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Gragg, William B. A note on an inverse eigenproblem for band matrices. Naval Postgraduate School, 1988.

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7

Bai, Z. On the conditioning of the nonsymmetric eigenproblem: theory and software. Courant Institute of Mathematical Sciences, New York University, 1989.

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Thurston, Gaylen A. Solution ofthe symmetric Eigenproblem AX=(Lambda)BX by delayed division. Langley Research Center, 1986.

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9

Borges, Carlos F. A parallel divide and conquer algorithm for the generalized real symmetric definite tridiagonal eigenproblem. Naval Postgraduate School, 1992.

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10

Gilboa, Guy. Nonlinear Eigenproblems in Image Processing and Computer Vision. Springer, 2018.

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Book chapters on the topic "Eigenproblems"

1

De Bie, Tijl, Nello Cristianini, and Roman Rosipal. "Eigenproblems in Pattern Recognition." In Handbook of Geometric Computing. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-28247-5_5.

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Pechstein, Clemens. "Adaptive BDDC Based on Local Eigenproblems." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56750-7_2.

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Ruhe, Axel. "Rational Krylov for Large Nonlinear Eigenproblems." In Applied Parallel Computing. State of the Art in Scientific Computing. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11558958_42.

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Voss, Heinrich. "A Jacobi–Davidson Method for Nonlinear Eigenproblems." In Computational Science - ICCS 2004. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24687-9_5.

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Bayly, B. J. "Infinitely Conducting Dynamos and other Horrible Eigenproblems." In Nonlinear Phenomena in Atmospheric and Oceanic Sciences. Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-0250-7_4.

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Voss, Heinrich. "Variational Principles for Eigenvalues of Nonlinear Eigenproblems." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10705-9_30.

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van der Hoeven, Joris, and Bernard Mourrain. "Efficient Certification of Numeric Solutions to Eigenproblems." In Mathematical Aspects of Computer and Information Sciences. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-72453-9_6.

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Auchmuty, Giles. "Variational Principles for Self-Adjoint Elliptic Eigenproblems." In Nonconvex Optimization and Its Applications. Springer US, 2001. http://dx.doi.org/10.1007/978-1-4613-0275-9_2.

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Basermann, Achim. "Parallel Preconditioned Solvers for Large Sparse Hermitian Eigenproblems." In Vector and Parallel Processing – VECPAR’98. Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/10703040_7.

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Maday, Yvon. "Numerical Analysis of Eigenproblems for Electronic Structure Calculations." In Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_258.

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Conference papers on the topic "Eigenproblems"

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SLEIJPEN, GERARD L. G., H. A. VAN DER VORST, and F. WUBS. "PRECONDITIONING FOR EIGENPROBLEMS." In Proceedings of the Fourth International Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814291071_0015.

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Kim, Ki-Ook. "Perturbation method in condensation for eigenproblems." In 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit. American Institute of Aeronautics and Astronautics, 1998. http://dx.doi.org/10.2514/6.1998-2018.

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Kim, Ki-Ook. "Improved hybrid dynamic condensation for eigenproblems." In 37th Structure, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 1996. http://dx.doi.org/10.2514/6.1996-1401.

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CHAHINIAN, LEON. "The method of Jacobi for unsymmetric eigenproblems." In 30th Structures, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 1989. http://dx.doi.org/10.2514/6.1989-1392.

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Eberlein, P. "The Parallel Solution Of Eigenproblems On Multiprocessor Systems." In 31st Annual Technical Symposium, edited by Franklin T. Luk. SPIE, 1988. http://dx.doi.org/10.1117/12.942027.

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Zhang, Yong-Qiang, and Wen-Liang Wang. "Eigenvector Derivatives of Generalized Nondefective Eigenproblems With Repeated Eigenvalues." In ASME 1993 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/93-gt-340.

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A new method is presented for computation of eigenvalue and eigenvector derivatives associated with repeated eigenvalues of the generalized nondefective eigenproblem. This approach is an extension of recent work by Dailey and by Juang et al. and is applicable to symmetric or nonsymmetric systems. The extended phases read as follows. The differentiable eigenvectors and their derivatives associated with repeated eigenvalues are determined for generalized eigenproblem, requiring the knowledge of only those eigenvectors to be differentiated. Moreover, formulations for computing eigenvector derivat

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Voss, Heinrich, Jiacong Yin, and Pu Chen. "Solving Huge Gyroscopic Eigenproblems With AMLS and Subspace Iteration." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-85517.

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The Automated Multilevel Sub-structuring (AMLS) method is a powerful technique for computing a large number of eigenpairs with moderate accuracy for huge definite eigenvalue problems in structural analysis. It also turned out to be a useful tool to construct a suitable ansatz space for orthogonal projection methods for gyroscopic problems. This paper takes advantage of information gained from AMLS to improve the obtained eigenpairs via a small number of subspace iteration steps.

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Sima, Vasile, and Peter Benner. "Pitfalls When Solving Eigenproblems - With Applications in Control Engineering." In 12th International Conference on Informatics in Control, Automation and Robotics. SCITEPRESS - Science and and Technology Publications, 2015. http://dx.doi.org/10.5220/0005533301710178.

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BASERMANN, A., and B. STEFFEN. "PARALLELIZATION STRATEGIES FOR SUBSPACE METHODS TO SOLVE LARGE EIGENPROBLEMS." In Proceedings of the Fourth International Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814291071_0014.

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AKL, F., and R. HACKETT. "A multi-frontal algorithm for parallel processing of large eigenproblems." In 27th Structures, Structural Dynamics and Materials Conference. American Institute of Aeronautics and Astronautics, 1986. http://dx.doi.org/10.2514/6.1986-929.

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Reports on the topic "Eigenproblems"

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Gragg, William, and L. Reichel. A Divide and Conquer Method for Unitary and Orthogonal Eigenproblems. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada205433.

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Ammar, G. S., W. B. Gragg, and L. Reichel. Direct and Inverse Unitary Eigenproblems in Signal Processing: An Overview. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada259348.

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Foulser, David E. A Blocked Jacobi Method for the Symmetric Eigenproblem. Defense Technical Information Center, 1989. http://dx.doi.org/10.21236/ada206553.

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Borges, Carlos F., and William B. Gragg. A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada262297.

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