Open AccessFilter factor analysis of scaled gradient methods for linear least squares
Author(s) -
Federica Porta,
Anastasia Cornelio,
Luca Zanni,
Marco Prato
Publication year - 2013
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/464/1/012006
Subject(s) - regularization (linguistics) , algorithm , least squares function approximation , filter (signal processing) , computer science , linear filter , iterative method , linear least squares , mathematical optimization , mathematics , scaling , recursive least squares filter , adaptive filter , artificial intelligence , singular value decomposition , statistics , estimator , computer vision , geometry
A typical way to compute a meaningful solution of a linear least squares problem involves the introduction of a filter factors array, whose aim is to avoid noise amplification due to the presence of small singular values. Beyond the classical direct regularization approaches, iterative gradient methods can be thought as filtering methods, due to their typical capability to recover the desired components of the true solution at the first iterations. For an iterative\udmethod, regularization is achieved by stopping the procedure before the noise introduces artifacts, making the iteration number playing the role of the regularization parameter. In this paper we want to investigate the filtering and regularizing effects of some first-order algorithms, showing in particular which benefits can be gained in recovering the filters of the true solution by means of a suitable scaling matrix