USING FRAMES OF SUBSPACES IN GALERKIN AND RICHARDSON METHODS FOR SOLVING OPERATOR EQUATIONS
Authors
Abstract:
In this paper, two iterative methods are constructed to solve the operator equation $ Lu=f $ where $L:Hrightarrow H $ is a bounded, invertible and self-adjoint linear operator on a separable Hilbert space $ H $. By using the concept of frames of subspaces, which is a generalization of frame theory, we design some algorithms based on Galerkin and Richardson methods, and then we investigate the convergence and optimality of them.
similar resources
Richardson and Chebyshev Iterative Methods by Using G-frames
In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern, Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper...
full textPreconditioned Galerkin and minimal residual methods for solving Sylvester equations
This paper presents preconditioned Galerkin and minimal residual algorithms for the solution of Sylvester equations AX XB = C. Given two good preconditioner matricesM and N for matrices A and B, respectively, we solve the Sylvester equations MAXN MXBN =MCN. The algorithms use the Arnoldi process to generate orthonormal bases of certain Krylov subspaces and simultaneously reduce the order of Syl...
full textdevelopment of different optical methods for determination of glucose using cadmium telluride quantum dots and silver nanoparticles
a simple, rapid and low-cost scanner spectroscopy method for the glucose determination by utilizing glucose oxidase and cdte/tga quantum dots as chromoionophore has been described. the detection was based on the combination of the glucose enzymatic reaction and the quenching effect of h2o2 on the cdte quantum dots (qds) photoluminescence.in this study glucose was determined by utilizing glucose...
Efficient Adaptive Stochastic Galerkin Methods for Parametric Operator Equations
This paper is concerned with the design and implementation of efficient solution algorithms for elliptic PDE problems with correlated random data. The energy orthogonality that is built into stochastic Galerkin approximations is cleverly exploited to give an innovative energy error estimation strategy that utilizes the tensor product structure of the approximation space. An associated error est...
full textConvergence of iterative methods for solving random operator equations
We discuss the concept of probabilistic quasi-nonexpansive mappings in connection with the mappings of Nishiura. We also prove a result regarding the convergence of the sequence of successive approximations for probabilistic quasi-nonexpansive mappings.
full textA matrix LSQR algorithm for solving constrained linear operator equations
In this work, an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$ and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$ where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$, $mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$, $ma...
full textMy Resources
Journal title
volume 4 issue 1
pages 25- 37
publication date 2017-06-19
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023