A direct method for sparse least squares problems with lower and upper bounds

1988 ◽  
Vol 54 (1) ◽  
pp. 19-32 ◽  
Author(s):  
�ke Bj�rck
Keyword(s):  
Least Squares ◽  
Direct Method ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Least Squares Problems ◽  
A Direct Method

Linear Least-Squares Computations Using Givens Transformations

1983 ◽  
Vol 37 (4) ◽  
pp. 225-233 ◽  
Author(s):  
J. A. R. Blais
Keyword(s):  
Least Squares ◽  
Error Estimates ◽  
Data Storage ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Direct Method ◽  
Linear Least Squares ◽  
Normal Equations ◽  
Estimation Problems ◽  
A Direct Method

Givens transformations provide a direct method for solving linear least-squares estimation problems without forming the normal equations. This approach has been shown to be particularly advantageous in recursive situations because of characteristics related to data storage requirements, numerical stability and computational efficiency. The following discussion will concentrate on the problem of updating least-squares parameter and error estimates using Givens transformations. Special attention will be given to photogrammetric and geodetic applications.

scholarly journals Condition numbers of the least squares problems with multiple right-hand sides

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1667-1676
Author(s):  
Lingsheng Meng ◽  
Bing Zheng
Keyword(s):  
Least Squares ◽  
Numerical Experiments ◽  
Upper Bounds ◽  
Condition Numbers ◽  
Least Squares Problems ◽  
Least Squares Problem ◽  
Right Hand

In this paper, we investigate the normwise, mixed and componentwise condition numbers of the least squares problem min X?Rnxd ||X - B||F, where A ? Rmxn is a rank-deficient matrix and B ? Rmxd. The closed formulas or upper bounds for these condition numbers are presented, which extend the earlier work for the least squares problem with single right-hand side (i.e. B ? b is an m-vector) of several authors. Numerical experiments are given to confirm our results.

Exponential Decay of Truncated Correlation Functions Via the Generating Function: A Direct Method

1998 ◽  
Vol 10 (04) ◽  
pp. 429-438 ◽  
Author(s):  
Gastão A. Braga ◽  
Paulo C. Lima ◽  
Michael L. O'Carroll
Keyword(s):  
Correlation Function ◽  
Ising Model ◽  
Exponential Decay ◽  
Direct Method ◽  
Polymer System ◽  
Lattice Models ◽  
Upper Bounds ◽  
Field Dependent ◽  
Contour Models ◽  
A Direct Method

We consider statistical mechanics lattice models where the external field dependent partition function can be represented as a standard polymer system. Using this polymer representation and elementary complex analytic arguments, we obtain upper bounds and give a simple proof on the uniform (in n) exponential decay of the n-point truncated correlation function. We illustrate the method by applying it to the high and low temperature Ising model and to contour models.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

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