The algebraic eigenvalue problem
The algebraic eigenvalue problem
Applied numerical linear algebra
Applied numerical linear algebra
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Matrix algorithms
Methods for Solving Systems of Nonlinear Equations
Methods for Solving Systems of Nonlinear Equations
Orthogonalization Via Deflation: A Minimum Norm Approach for Low-Rank Approximations of a Matrix
SIAM Journal on Matrix Analysis and Applications
Hi-index | 7.29 |
The problems of calculating a dominant eigenvector or a dominant pair of singular vectors, arise in several large scale matrix computations. In this paper we propose a minimum norm approach for solving these problems. Given a matrix, A, the new method computes a rank-one matrix that is nearest to A, regarding the Frobenius matrix norm. This formulation paves the way for effective minimization techniques. The methods proposed in this paper illustrate the usefulness of this idea. The basic iteration is similar to that of the power method, but the rate of convergence is considerably faster. Numerical experiments are included.