How can we speed up matrix multiplication?
SIAM Review
Direct methods for sparse matrices
Direct methods for sparse matrices
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
An improved Newton interaction for the generalized inverse of a Matrix, with applications
SIAM Journal on Scientific and Statistical Computing
Highly parallel sparse Cholesky factorization
SIAM Journal on Scientific and Statistical Computing
Fast and efficient parallel solution of sparse linear systems
SIAM Journal on Computing
Fast Gaussian elimination with partial pivoting for matrices with displacement structure
Mathematics of Computation
Matrix computations (3rd ed.)
Modular arithmetic for linear algebra computations in the real field
Journal of Symbolic Computation
Matrix algorithms
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Design, implementation and testing of extended and mixed precision BLAS
ACM Transactions on Mathematical Software (TOMS)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Approximate algorithms to derive exact solutions to systems of linear equations
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Accurate and Efficient Floating Point Summation
SIAM Journal on Scientific Computing
The aggregation and cancellation techniques as a practical tool for faster matrix multiplication
Theoretical Computer Science - Algebraic and numerical algorithm
SIAM Journal on Scientific Computing
Additive preconditioning and aggregation in matrix computations
Computers & Mathematics with Applications
Schur aggregation for linear systems and determinants
Theoretical Computer Science
A new error-free floating-point summation algorithm
Computers & Mathematics with Applications
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According to our previous theoretical and experimental study, additive preconditioners can be readily computed for ill conditioned matrices, but application of such preconditioners to facilitating matrix computations is not straight-forward. In the present paper we develop some nontrivial techniques for this task.They enabled us to con ne the original numerical problems to the computation of the Schur aggregates of smaller sizes. We overcome these problems by extending the Wilkinson's iterative re nement and applying some advanced semi-symbolic algorithms for multiplication and summation.In particular with these techniques we control precision throughout our computations.