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.
An Error Resilience Strategy of a Complex Moment-Based Eigensolver:
Akira Imakura, Yasunori Futamura, and Tetsuya Sakurai.- Numerical Integral
Eigensolver for a Ring Region on the Complex Plane: Yasuyuki Maeda, Tetsuya
Sakurai, James Charles, Michael Povolotskyi, Gerhard Klimeck, and Jose E.
Roman.- A Parallel Bisection and Inverse Iteration Solver for a Subset of
Eigenpairs of Symmetric Band Matrices: Hiroyuki Ishigami, Hidehiko Hasegawa,
Kinji Kimura, and Yoshimasa Nakamura.- The Flexible ILU Preconditioning for
Solving Large Nonsymmetric Linear Systems of Equations: Takatoshi Nakamura
and Takashi Nodera.- Improved Coefficients for Polynomial Filtering in ESSEX:
Martin Galgon, Lukas Krämer, Bruno Lang, Andreas Alvermann, Holger Fehske,
Andreas Pieper, Georg Hager, Moritz Kreutzer, Faisal Shahzad, Gerhard
Wellein, Achim Basermann, Melven Röhrig-Zöllner, and Jonas Thies.-
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, and Tetsuya Sakurai.- Properties of Definite BetheSalpeter
Eigenvalue Problems: Meiyue Shao and Chao Yang.- Preconditioned Iterative
Methods for Eigenvalue Counts: Eugene Vecharynski and Chao Yang.- Comparison
of Tridiagonalization Methods using High-precision Arithmetic with MuPAT:
Ryoya Ino, Kohei Asami, Emiko Ishiwata, and Hidehiko Hasegawa.- Computation
of Eigenvectors for a Specially Structured Banded Matrix: Hiroshi Takeuchi,
Kensuke Aihara, Akiko Fukuda, and Emiko Ishiwata.- 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, and Yoshimasa Nakamura.- Accuracy Improvement of the Shifted
Block BiCGGR Method for Linear Systems with Multiple Shifts and Multiple
Right-Hand Sides: Hiroto Tadano, Shusaku Saito, and Akira Imakura.-
Memory-Saving Technique for the SakuraiSugiura Eigenvalue Solver using the
Shifted Block Conjugate Gradient Method: Yasunori Futamura and Tetsuya
Sakurai.- Filter Diagonalization Method by Using a Polynomial of a Resolvent
as the Filter for a Real Symmetric-Definite Generalized Eigenproblem: Hiroshi
Murakami.- Off-Diagonal Perturbation, First-Order Approximation and Quadratic
Residual Bounds for Matrix Eigenvalue Problems: Yuji Nakatsukasa.- An
Elementary Derivation of the Projection Method for Nonlinear Eigenvalue
Problems Based on Complex Contour Integration: Yusaku Yamamoto.- Fast
Multipole Method as a Matrix-Free Hierarchical Low-Rank Approximation: Rio
Yokota, Huda Ibeid, and David Keyes.- Recent Progress in Linear Response
Eigenvalue Problems: Zhaojun Bai and Ren-Cang Li.
