Optimal Approximation of Linear Operators: a Singular Value Decomposition Approach
نویسندگان
چکیده
The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized singular values are derived and the problem of optimal rank approximation of linear operators is investigated in this context. We give sufficient conditions for the existence of optimal rank approximants in the p-induced norm and discuss an application of generalized singular values for the identification of dynamical systems from data.
منابع مشابه
Solving linear and nonlinear optimal control problem using modified adomian decomposition method
First Riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. An analytical approximation of the solution of nonlinear differential Riccati equation is investigated using the Adomian decomposition method. An application in optimal control is presented. The solution in different order of approximations and different methods of approximat...
متن کاملChange Point Estimation of the Stationary State in Auto Regressive Moving Average Models, Using Maximum Likelihood Estimation and Singular Value Decomposition-based Filtering
In this paper, for the first time, the subject of change point estimation has been utilized in the stationary state of auto regressive moving average (ARMA) (1, 1). In the monitoring phase, in case the features of the question pursue a time series, i.e., ARMA(1,1), on the basis of the maximum likelihood technique, an approach will be developed for the estimation of the stationary state’s change...
متن کاملFace Recognition Based Rank Reduction SVD Approach
Standard face recognition algorithms that use standard feature extraction techniques always suffer from image performance degradation. Recently, singular value decomposition and low-rank matrix are applied in many applications,including pattern recognition and feature extraction. The main objective of this research is to design an efficient face recognition approach by combining many tech...
متن کاملOn the optimal approximation for the symmetric Procrustes problems of the matrix equation AXB = C
The explicit analytical expressions of the optimal approximation solutions for the symmetric Procrustes problems of the linear matrix equation AXB = C are derived, with the projection theorem in Hilbert space , the quotient singular value decomposition (QSVD) and the canonical correlation decomposition (CCD) being used.
متن کاملModified Laplace Decomposition Method for Singular IVPs in the second-Order Ordinary Differential Equations
In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems
متن کامل