Solving Least Squares for Linear Equations over Strongly Connected Directed Networks

2020 ◽  
Author(s):  
Mohammad Jahvani ◽  
Martin Guay
Keyword(s):  
Least Squares ◽  
Linear Equations ◽  
Directed Networks ◽  
Strongly Connected

A Nonlinear Least-Squares Graphical Tool (‘Gaussfit’) for Educational Purposes

2010 ◽  
Vol 47 (1) ◽  
pp. 11-22 ◽  
Author(s):  
Krešimir Malarić ◽  
Roman Malarić ◽  
Hrvoje Hegeduš
Keyword(s):  
Least Squares ◽  
Input Data ◽  
Least Squares Method ◽  
Linear Equations ◽  
Computer Calculation ◽  
Nonlinear Least Squares ◽  
Undergraduate Level ◽  
Graphical Tool ◽  
Systems Of Linear Equations ◽  
Graphical Presentation

This paper describes a computer program that finds a function which closely approximates experimental data using the least-squares method. The program finds parameters of the function as well as their corresponding uncertainties. It also has a subroutine for graphical presentation of the input data and the function. The program is used for educational purposes at undergraduate level for students who are learning least-squares fitting, how to solve systems of linear equations and about computer calculation errors.

scholarly journals A Representation of Nonhomogeneous Quadratic Forms with Application to the Least Squares Solution

2011 ◽  
Vol 2011 ◽  
pp. 1-5 ◽  
Author(s):  
Czesław Stępniak
Keyword(s):  
Least Squares ◽  
Quadratic Forms ◽  
Differential Calculus ◽  
Linear Models ◽  
Linear Equations ◽  
Algebraic Approach ◽  
System Of Linear Equations ◽  
Least Squares Solution ◽  
Inconsistent System ◽  
Usual Solution

The least squares problem appears, among others, in linear models, and it refers to inconsistent system of linear equations. A crucial question is how to reduce the least squares solution in such a system to the usual solution in a consistent one. Traditionally, this is reached by differential calculus. We present a purely algebraic approach to this problem based on some identities for nonhomogeneous quadratic forms.

On Least Squares Solutions of Linear Equations

1961 ◽  
Vol 8 (4) ◽  
pp. 628-636 ◽  
Author(s):  
E. E. Osborne
Keyword(s):  
Least Squares ◽  
Linear Equations
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