Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing: EPASA 2015, Tsukuba, Japan, September 2015

Description

This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems. Front Matter ....Pages i-x An Error Resilience Strategy of a Complex Moment-Based Eigensolver (Akira Imakura, Yasunori Futamura, Tetsuya Sakurai)....Pages 1-18 Numerical Integral Eigensolver for a Ring Region on the Complex Plane (Yasuyuki Maeda, Tetsuya Sakurai, James Charles, Michael Povolotskyi, Gerhard Klimeck, Jose E. Roman)....Pages 19-30 A Parallel Bisection and Inverse Iteration Solver for a Subset of Eigenpairs of Symmetric Band Matrices (Hiroyuki Ishigami, Hidehiko Hasegawa, Kinji Kimura, Yoshimasa Nakamura)....Pages 31-50 The Flexible ILU Preconditioning for Solving Large Nonsymmetric Linear Systems of Equations (Takatoshi Nakamura, Takashi Nodera)....Pages 51-61 Improved Coefficients for Polynomial Filtering in ESSEX (Martin Galgon, Lukas Krämer, Bruno Lang, Andreas Alvermann, Holger Fehske, Andreas Pieper et al.)....Pages 63-79 Eigenspectrum Calculation of the O(a)-Improved Wilson-Dirac Operator in Lattice QCD Using the Sakurai-Sugiura Method (Hiroya Suno, Yoshifumi Nakamura, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Yasunori Futamura, Akira Imakura et al.)....Pages 81-90 Properties of Definite Bethe–Salpeter Eigenvalue Problems (Meiyue Shao, Chao Yang)....Pages 91-105 Preconditioned Iterative Methods for Eigenvalue Counts (Eugene Vecharynski, Chao Yang)....Pages 107-123 Comparison of Tridiagonalization Methods Using High-Precision Arithmetic with MuPAT (Ryoya Ino, Kohei Asami, Emiko Ishiwata, Hidehiko Hasegawa)....Pages 125-141 Computation of Eigenvectors for a Specially Structured Banded Matrix (Hiroshi Takeuchi, Kensuke Aihara, Akiko Fukuda, Emiko Ishiwata)....Pages 143-155 Monotonic Convergence to Eigenvalues of Totally Nonnegative Matrices in an Integrable Variant of the Discrete Lotka-Volterra System (Akihiko Tobita, Akiko Fukuda, Emiko Ishiwata, Masashi Iwasaki, Yoshimasa Nakamura)....Pages 157-169 Accuracy Improvement of the Shifted Block BiCGGR Method for Linear Systems with Multiple Shifts and Multiple Right-Hand Sides (Hiroto Tadano, Shusaku Saito, Akira Imakura)....Pages 171-185 Memory-Saving Technique for the Sakurai–Sugiura Eigenvalue Solver Using the Shifted Block Conjugate Gradient Method (Yasunori Futamura, Tetsuya Sakurai)....Pages 187-203 Filter Diagonalization Method by Using a Polynomial of a Resolvent as the Filter for a Real Symmetric-Definite Generalized Eigenproblem (Hiroshi Murakami)....Pages 205-232 Off-Diagonal Perturbation, First-Order Approximation and Quadratic Residual Bounds for Matrix Eigenvalue Problems (Yuji Nakatsukasa)....Pages 233-249 An Elementary Derivation of the Projection Method for Nonlinear Eigenvalue Problems Based on Complex Contour Integration (Yusaku Yamamoto)....Pages 251-265 Fast Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation (Rio Yokota, Huda Ibeid, David Keyes)....Pages 267-286 Recent Progress in Linear Response Eigenvalue Problems (Zhaojun Bai, Ren-Cang Li)....Pages 287-304 Back Matter ....Pages 305-313