Application of the new method for the solution of the linear least squares problem

2005 ◽  
pp. 82-87
Keyword(s):  
Least Squares ◽  
New Method ◽  
Linear Least Squares ◽  
Least Squares Problem ◽  
Linear Least Squares Problem

scholarly journals On weighted Strand’s iteration

2018 ◽  
Vol 34 (2) ◽  
pp. 183-190
Author(s):  
D. CARP ◽  
◽  
C. POPA ◽  
T. PRECLIK ◽  
U. RUDE ◽  
...  
Keyword(s):  
Iterative Method ◽  
Least Squares ◽  
Numerical Approximation ◽  
Iterative Algorithms ◽  
Linear Least Squares ◽  
Minimal Norm ◽  
Least Squares Problem ◽  
Minimal Norm Solution ◽  
Linear Least Squares Problem

In this paper we present a generalization of Strand’s iterative method for numerical approximation of the weighted minimal norm solution of a linear least squares problem. We prove convergence of the extended algorithm, and show that previous iterative algorithms proposed by L. Landweber, J. D. Riley and G. H. Golub are particular cases of it.

Seismic data interpolation beyond aliasing using regularized nonstationary autoregression

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. V69-V77 ◽  
Author(s):  
Yang Liu ◽  
Sergey Fomel
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Irregular Sampling ◽  
Linear Least Squares ◽  
New Approach ◽  
Least Squares Problem ◽  
Linear Least Squares Problem ◽  
Imaging Results ◽  
Regularization Parameters ◽  
Selection Of

Seismic data are often inadequately or irregularly sampled along spatial axes. Irregular sampling can produce artifacts in seismic imaging results. We have developed a new approach to interpolate aliased seismic data based on adaptive prediction-error filtering (PEF) and regularized nonstationary autoregression. Instead of cutting data into overlapping windows (patching), a popular method for handling nonstationarity, we obtain smoothly nonstationary PEF coefficients by solving a global regularized least-squares problem. We employ shaping regularization to control the smoothness of adaptive PEFs. Finding the interpolated traces can be treated as another linear least-squares problem, which solves for data values rather than filter coefficients. Compared with existing methods, the advantages of the proposed method include an intuitive selection of regularization parameters and fast iteration convergence. The technique was tested on benchmark synthetic and field data to prove it can successfully reconstruct data with decimated or missing traces.

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