The algebraic eigenvalue problem
The algebraic eigenvalue problem
ACM Transactions on Mathematical Software (TOMS)
Algorithm 694: a collection of test matrices in MATLAB
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem
SIAM Journal on Matrix Analysis and Applications
Test matrices for regularization methods
SIAM Journal on Scientific Computing
A Divide-and-Conquer Algorithm for the Symmetric TridiagonalEigenproblem
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Applied numerical linear algebra
Applied numerical linear algebra
Computing an Eigenvector with Inverse Iteration
SIAM Review
The symmetric eigenvalue problem
The symmetric eigenvalue problem
A new O (N(2)) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem
A new O (N(2)) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Numerical computing with IEEE floating point arithmetic
Numerical computing with IEEE floating point arithmetic
A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
Orthogonal Eigenvectors and Relative Gaps
SIAM Journal on Matrix Analysis and Applications
A Portable Programming Interface for Performance Evaluation on Modern Processors
International Journal of High Performance Computing Applications
Orthogonal polynomials (in Matlab)
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Glued Matrices and the MRRR Algorithm
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The design and implementation of the MRRR algorithm
ACM Transactions on Mathematical Software (TOMS)
Benefits of IEEE-754 Features in Modern Symmetric Tridiagonal Eigensolvers
SIAM Journal on Scientific Computing
ACM Transactions on Mathematical Software (TOMS)
MR3-SMP: A symmetric tridiagonal eigensolver for multi-core architectures
Parallel Computing
Divide and Conquer on Hybrid GPU-Accelerated Multicore Systems
SIAM Journal on Scientific Computing
dqds with Aggressive Early Deflation
SIAM Journal on Matrix Analysis and Applications
Detecting Localization in an Invariant Subspace
SIAM Journal on Scientific Computing
A shift strategy for superquadratic convergence in the dqds algorithm for singular values
Journal of Computational and Applied Mathematics
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LAPACK is often mentioned as a positive example of a software library that encapsulates complex, robust, and widely used numerical algorithms for a wide range of applications. At installation time, the user has the option of running a (limited) number of test cases to verify the integrity of the installation process. On the algorithm developer's side, however, more exhaustive tests are usually performed to study algorithm behavior on a variety of problem settings and also computer architectures. In this process, difficult test cases need to be found that reflect particular challenges of an application or push algorithms to extreme behavior. These tests are then assembled into a comprehensive collection, therefore making it possible for any new or competing algorithm to be stressed in a similar way. This article describes an infrastructure for exhaustively testing the symmetric tridiagonal eigensolvers implemented in LAPACK. It consists of two parts: a selection of carefully chosen test matrices with particular idiosyncrasies and a portable testing framework that allows for easy testing and data processing. The tester facilitates experiments with algorithmic choices, parameter and threshold studies, and performance comparisons on different architectures.