Abstract
The linear inverse problem is discretized to be an n-dimensional ill-posed linear equations system . In the present paper, an invariant manifold defined in terms of the square norm of a residual vector is used to derive an iterative algorithm with a fast descent direction , which is close to, but not exactly equal to, the best descent direction . The matrix is obtained by using a vector regularization method together with a matrix conjugate gradient method to find the right inversion of : . The vector regularization iterative algorithm is proven to be Lyapunov stable, and the direct inversion method with solution expressed by converges fast. The accuracy and efficiency of them are verified through the numerical tests of linear inverse problems under a large random noise.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
