منابع مشابه
Randomized Block Kaczmarz Method with Projection for Solving Least Squares
The Kaczmarz method is an iterative method for solving overcomplete linear systems of equations Ax = b. The randomized version of the Kaczmarz method put forth by Strohmer and Vershynin iteratively projects onto a randomly chosen solution space given by a single row of the matrix A and converges exponentially in expectation to the solution of a consistent system. In this paper we analyze two bl...
متن کاملPaved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method
The block Kaczmarz method is an iterative scheme for solving overdetermined least-squares problems. At each step, the algorithm projects the current iterate onto the solution space of a subset of the constraints. This paper describes a block Kaczmarz algorithm that uses a randomized control scheme to choose the subset at each step. This algorithm is the first block Kaczmarz method with an (expe...
متن کاملThe Randomized Kaczmarz Method with Mismatched Adjoint
This paper investigates the randomized version of the Kaczmarz method to solve linear systems in the case where the adjoint of the system matrix is not exact—a situation we refer to as “mismatched adjoint”. We show that the method may still converge both in the overand underdetermined consistent case under appropriate conditions, and we calculate the expected asymptotic rate of linear convergen...
متن کاملRandomized Sparse Block Kaczmarz as Randomized Dual Block-Coordinate Descent
We show that the Sparse Kaczmarz method is a particular instance of the coordinate gradient method applied to an unconstrained dual problem corresponding to a regularized `1-minimization problem subject to linear constraints. Based on this observation and recent theoretical work concerning the convergence analysis and corresponding convergence rates for the randomized block coordinate gradient ...
متن کاملComments on the randomized Kaczmarz method
In this short note we respond to some concerns raised by Y. Censor, G. Herman, and M. Jiang about the randomized Kaczmarz method that we proposed in [5]. The Kaczmarz method is a well-known iterative algorithm for solving a linear system of equations Ax = b. For more than seven decades, this method was useful in practical applications, and it was studied in many research papers. Despite of this...
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ژورنال
عنوان ژورنال: Journal of Mathematical Imaging and Vision
سال: 2014
ISSN: 0924-9907,1573-7683
DOI: 10.1007/s10851-014-0539-7