The algebraic eigenvalue problem
The algebraic eigenvalue problem
Average-case stability of Gaussian elimination
SIAM Journal on Matrix Analysis and Applications
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Applied numerical linear algebra
Applied numerical linear algebra
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
SIAM Journal on Scientific Computing
A Truncated RQ Iteration for Large Scale Eigenvalue Calculations
SIAM Journal on Matrix Analysis and Applications
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Matrix algorithms
A Chebyshev-Davidson Algorithm for Large Symmetric Eigenproblems
SIAM Journal on Matrix Analysis and Applications
The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods
| Hi-index | 7.29 |
The shift-and-invert method is very efficient in eigenvalue computations, in particular when interior eigenvalues are sought. This method involves solving linear systems of the form (A-@sI)z=b. The shift @s is variable, hence when a direct method is used to solve the linear system, the LU factorization of (A-@sI) needs to be computed for every shift change. We present two strategies that reduce the number of floating point operations performed in the LU factorization when the shift changes. Both methods perform first a preprocessing step that aims at eliminating parts of the matrix that are not affected by the diagonal change. This leads to about 43% and 50% flops savings respectively for the dense matrices.