Paper Info
Title
A refinement of an iterative orthogonal projection method.
Abstract
The Kaczmarz algorithm is an iterative orthogonal projection method for solving linear systems of equations. As compared to direct methods such as Gaussian elimination or sparse QR-factorization, this algorithm is efficient for problems with sparse matrices, as they appear in constraint-based User Interface (UI) layout specifications. We present a variant of the Kaczmarz method for solving non-square systems that can be applied to Graphical User Interface (GUI) layout problems. In its original form the Kaczmarz algorithm cannot handle soft constraints. Therefore, we propose two algorithms for handling specifications containing soft constraints using prioritized irreducible infeasible subsystem (IIS) detection and prioritized grouping constraints. If we use Kaczmarz during resizing of a window in a GUI then the system can also be under-determined. In this case, space is not distributed in an aesthetically pleasing way. To distribute the space according to the preferred size of the layout, we introduce the least squares Kaczmarz method to get the desired results.
Year
DOI
Venue
2018
10.1016/j.cam.2018.02.025
Journal of Computational and Applied Mathematics
Keywords
Field
DocType
UI layout,Kaczmarz algorithm,Soft constraints,Least squares,Cooling function
Mathematical optimization,Orthographic projection,Linear system,Kaczmarz method,Linear programming,Gaussian elimination,Solver,User interface,Mathematics,Sparse matrix
Journal
Volume
ISSN
Citations 
341
0377-0427
0
PageRank 
References 
Authors
0.34
8
4
Name
Order
Citations
PageRank
Noreen Jamil1126.01
Farhaan Mirza23812.06
M. Asif Naeem310219.73
Nilufar Baghaei422726.75