The WY representation for products of householder matrices
SIAM Journal on Scientific and Statistical Computing - Papers from the Second Conference on Parallel Processing for Scientific Computin
Solution of large, dense symmetric generalized eigenvalue problems using secondary storage
ACM Transactions on Mathematical Software (TOMS)
A storage-efficient WY representation for products of householder transformations
SIAM Journal on Scientific and Statistical Computing
An adaptive blocking strategy for matrix factorizations
CONPAR 90 Proceedings of the joint international conference on Vector and parallel processing
A parallel algorithm for reducing symmetric banded matrices to tridiagonal form
SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)
Using Level 3 BLAS in Rotation-Based Algorithms
SIAM Journal on Scientific Computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Banded Eigenvalue Solvers on Vector Machines
ACM Transactions on Mathematical Software (TOMS)
Band reduction algorithms revisited
ACM Transactions on Mathematical Software (TOMS)
Algorithm 807: The SBR Toolbox—software for successive band reduction
ACM Transactions on Mathematical Software (TOMS)
Data Structures and Algorithms
Data Structures and Algorithms
Automatically Tuned Linear Algebra Software
Automatically Tuned Linear Algebra Software
Band reduction algorithms revisited
ACM Transactions on Mathematical Software (TOMS)
Algorithm 807: The SBR Toolbox—software for successive band reduction
ACM Transactions on Mathematical Software (TOMS)
Block algorithms for reordering standard and generalized Schur forms
ACM Transactions on Mathematical Software (TOMS)
Parallel block tridiagonalization of real symmetric matrices
Journal of Parallel and Distributed Computing
Time-memory trade-offs using sparse matrix methods for large-scale eigenvalue problems
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
Prospectus for the next LAPACK and ScaLAPACK libraries
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Communication avoiding successive band reduction
Proceedings of the 17th ACM SIGPLAN symposium on Principles and Practice of Parallel Programming
Efficient reduction from block hessenberg form to hessenberg form using shared memory
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Computing eigenvectors of block tridiagonal matrices based on twisted block factorizations
Journal of Computational and Applied Mathematics
Divide and Conquer on Hybrid GPU-Accelerated Multicore Systems
SIAM Journal on Scientific Computing
Efficient generalized Hessenberg form and applications
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.00 |
We develop an algorithmic framework for reducing the bandwidth of symmetric matrices via orthogonal similarity transformations. This framework includes the reduction of full matrices to banded or tridiagonal form and the reduction of banded matrices to narrower banded or tridiagonal form, possibly in multiple steps. Our framework leads to algorithms that require fewer floating-point operations than do standard algorithms, if only the eigenvalues are required. In addition, it allows for space-time tradeoffs and enables or increases the use of blocked transformations.