How can we speed up matrix multiplication?
SIAM Review
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
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
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Matrix algorithms
Structured matrices and polynomials: unified superfast algorithms
Structured matrices and polynomials: unified superfast algorithms
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
An iterated eigenvalue algorithm for approximating roots of univariate polynomials
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
The aggregation and cancellation techniques as a practical tool for faster matrix multiplication
Theoretical Computer Science - Algebraic and numerical algorithm
Effect of small rank modification on the condition number of a matrix
Computers & Mathematics with Applications
Additive preconditioning and aggregation in matrix computations
Computers & Mathematics with Applications
Eigen-solving via reduction to DPR1 matrices
Computers & Mathematics with Applications
Schur aggregation for linear systems and determinants
Theoretical Computer Science
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We propose and analyze additive preprocessing for computing a vector in the null space of a matrix and a basis for this space. Due to our preprocessing, instead of singular linear systems we solve nonsingular ones, which preserve the conditioning properties and the structure of the input matrices. We extend our preprocessing to decrease the size and the condition number of an ill conditioned input matrix. We also cover applications to the eigenspace computations and to generating effective preconditioners for a linear system of equations.