منابع مشابه
A randomized Kaczmarz algorithm with exponential convergence
The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical estimates for its rate of convergence are still scarce. We introduce a randomized version of the Kaczmarz method for consistent, overdetermined linear system...
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 Extended Kaczmarz for Solving Least-Squares
We present a randomized iterative algorithm that exponentially converges in expectation to the minimum Euclidean norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate of given accuracy is proportional to the square condition number of the system multiplied by the number of non-zeros entries of the input mat...
متن کاملRandomized 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 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: BIT Numerical Mathematics
سال: 2020
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-020-00824-1