Sequential and Parallel Algorithms for the Inverse Toeplitz Singular Value Problem
نویسندگان
چکیده
When the Inverse Additive Singular Value Problem (IASVP) involves Toeplitz–type matrices it is possible to exploit this special structure to reduce the execution time. In this paper, we present two iterative local and global convergent algorithms (MIIIT and LPT) to solve efficiently the IASVP when the matrix is Toeplitz (IASVPT). As it will be shown, it can be achieved an asymptotic complexity one order of magnitude less than those algorithms that do not exploit the Toeplitz–like structure. Furthermore, we have implemented a parallel version of these both algorithms, called PMIIIT and PLPT, respectively, that highly reduce the execution time of the sequential algorithm at sight of the experiments. Keywords– Parallel programming, Inverse Singular Value Problem, Toeplitz matrices, Newton type methods, Least squares problem
منابع مشابه
On Some Inverse Singular Value Problems with Toeplitz-Related Structure
In this paper, we consider some inverse singular value problems for Toeplitz-related matrices. We construct a Toeplitz-plus-Hankel matrix from prescribed singular values including a zero singular value. Then we find a solution to the inverse singular value problem for Toeplitz matrices which have double singular values including a double zero singular value.
متن کاملParallelization of a Method for the Solution of the Inverse Additive Singular Value Problem
This paper describes the parallelization of a method (proposed by Chu in [7]) to solve the Inverse Additive Singular Value Problem (IASVP). The IASVP is a problem whose solution requires a high computational cost, both in time and in memory. For example, the complexity of Chu’s method is O(n) in time and O(n) in memory. Using parallel computing, the time needed to solve the problem has been sub...
متن کاملروشهای تجزیه مقادیر منفرد منقطع و تیخونوف تعمیمیافته در پایدارسازی مسئله انتقال به سمت پائین
The methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. Practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. In the geoid computations witho...
متن کاملOn inverse problem for singular Sturm-Liouville operator with discontinuity conditions
In this study, properties of spectral characteristic are investigated for singular Sturm-Liouville operators in the case where an eigen parameter not only appears in the differential equation but is also linearly contained in the jump conditions. Also Weyl function for considering operator has been defined and the theorems which related to uniqueness of solution of inverse proble...
متن کاملA Schur–based algorithm for computing the smallest eigenvalue of a symmetric positive definite Toeplitz matrix
Recent progress in signal processing and estimation has generated considerable interest in the problem of computing the smallest eigenvalue of symmetric positive definite Toeplitz matrices. Several algorithms have been proposed in the literature. Many of them compute the smallest eigenvalue in an iterative fashion, relying on the Levinson–Durbin solution of sequences of Yule–Walker systems. Exp...
متن کامل