Cubically Convergent Iterations for Invariant Subspace Computation
Copyright policy )Cubically Convergent Iterations for Invariant Subspace Computation
Summary: We propose a Newton-like iteration that evolves on the set of fixed dimensional subspaces of \(\mathbb R^n\) and converges locally cubically to the invariant subspaces of a symmetric matrix. This iteration is compared in terms of numerical cost and global behavior with three other methods that display the same property of cubic convergence. Moreover, we consider heuristics that greatly improve the global behavior of the iterations.
- Australian National University Australia
- University of Liège Belgium
- Florida State University United States
Optimization, Numerical computation of eigenvalues and eigenvectors of matrices, symmetric eigenproblem, inverse iteration, Physique, chimie, mathématiques & sciences de la terre, Global convergence, Matrix algebra, Keywords: Data coding, Invariant subspace, Physical, chemical, mathematical & earth Sciences, invariant subspace, Computational methods, Mathematical operators, Grassmann manifold, Inverse iteration, Eigenvalues and eigenfunctions, numerical examples, Newton equations, cubic convergence, Symmetric eigenproblem, Set theo Cubic convergence, Rayleigh quotient, global convergence, Normalization, Mathématiques, Newton method, Data compression, Jacobi-Davidson method, Heuristic methods, Algorithms, Riccati equations, Mathematics
Optimization, Numerical computation of eigenvalues and eigenvectors of matrices, symmetric eigenproblem, inverse iteration, Physique, chimie, mathématiques & sciences de la terre, Global convergence, Matrix algebra, Keywords: Data coding, Invariant subspace, Physical, chemical, mathematical & earth Sciences, invariant subspace, Computational methods, Mathematical operators, Grassmann manifold, Inverse iteration, Eigenvalues and eigenfunctions, numerical examples, Newton equations, cubic convergence, Symmetric eigenproblem, Set theo Cubic convergence, Rayleigh quotient, global convergence, Normalization, Mathématiques, Newton method, Data compression, Jacobi-Davidson method, Heuristic methods, Algorithms, Riccati equations, Mathematics
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