Handbook Series Linear Algebra. Eigenvectors of Real and Complex Matrices by L R and QR triangularizations.
Handbook Series Linear Algebra. Simultaneous Iteration Method for Symmetric Matrices.
Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem.
Harmonic Ritz and Lehmann bounds.
High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems.
Homogeneous Jacobi-Davidson.
Homotopy Algorithm for Symmetric Eigenvalue Problems.
Householder's Method for Complex Matrices and Eigensystems of Hermitian Matrices.
H-Splittings and two-stage iterative methods.
Hybrid Algorithm for Fast Toeplitz Orthogonalization.
IDR explained.
Image restoration through subimages and confidence images.
Implementation of the gmr algorithm for large symmetric eigenproblems
Implementing parallel elliptic solver on a Beowulf cluster.
Improved convergence bounds for smoothed aggregation method: linear dependence of the convergence rate on the number of levels
The smoothed aggregation method has became a widely used tool for solving the linear systems arising by the discretization of elliptic partial differential equations and their singular perturbations. The smoothed aggregation method is an algebraic multigrid technique where the prolongators are constructed in two steps. First, the tentative prolongator is constructed by the aggregation (or, the generalized aggregation) method. Then, the range of the tentative prolongator is smoothed by a sparse linear...
Improved convergence estimate for a multiply polynomially smoothed two-level method with an aggressive coarsening
A variational two-level method in the class of methods with an aggressive coarsening and a massive polynomial smoothing is proposed. The method is a modification of the method of Section 5 of Tezaur, Vaněk (2018). Compared to that method, a significantly sharper estimate is proved while requiring only slightly more computational work.
Improved initialization of the accelerated and robust QR-like polynomial root-finding.
Improving backward stability of Sakurai-Sugiura method with balancing technique in polynomial eigenvalue problem
One of the most efficient methods for solving the polynomial eigenvalue problem (PEP) is the Sakurai-Sugiura method with Rayleigh-Ritz projection (SS-RR), which finds the eigenvalues contained in a certain domain using the contour integral. The SS-RR method converts the original PEP to a small projected PEP using the Rayleigh-Ritz projection. However, the SS-RR method suffers from backward instability when the norms of the coefficient matrices of the projected PEP vary widely. To improve the backward...
Inclusion Theorems for a Section of a Matrix.
Incremental unknowns for solving partial differential equations.