Some iterative methods related to Frobenius norm minimization
نویسندگان
چکیده
منابع مشابه
Frobenius norm minimization and probing for preconditioning
In this paper we introduce a new method for defining preconditioners for the iterative solution of a system of linear equations. By generalizing the class of modified preconditioners (e.g. MILU), the interface probing, and the class of preconditioners related to the Frobenius norm minimization (e.g. FSAI, SPAI) we develop a toolbox for computing preconditioners that are improved relative to a g...
متن کاملImproving approximate inverses based on Frobenius norm minimization
Approximate inverses, based on Frobenius norm minimization, of real nonsingular matrices are analyzed from a purely theoretical point of view. In this context, this paper provides several sufficient conditions, that assure us the possibility of improving (in the sense of the Frobenius norm) some given approximate inverses. Moreover, the optimal approximate inverses of matrix A ∈ R, among all ma...
متن کاملPenalty Decomposition Methods for $L0$-Norm Minimization
In this paper we consider general l0-norm minimization problems, that is, the problems with l0-norm appearing in either objective function or constraint. In particular, we first reformulate the l0-norm constrained problem as an equivalent rank minimization problem and then apply the penalty decomposition (PD) method proposed in [33] to solve the latter problem. By utilizing the special structur...
متن کاملSome first order algorithms for `1/nuclear norm minimization
In the last decade, the problems related to l1/nuclear norm minimization attract a lot of attention in Signal Processing, Machine Learning and Optimization communities. In this paper, devoted to `1/nuclear norm minimization as “optimization beasts,” we give a detailed description of two attractive First Order optimization techniques for solving the problems of this type. The first one, aimed pr...
متن کاملSparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism
We consider preconditioning strategies for the iterative solution of dense complex symmetric nonHermitian systems arising in computational electromagnetics. We consider in particular sparse approximate inverse preconditioners that use a static nonzero pattern selection. The novelty of our approach comes from using a di erent nonzero pattern selection for the original matrix from that for the pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1991
ISSN: 0898-1221
DOI: 10.1016/0898-1221(91)90199-e