Chebyshev Solution of an Inconsistent System of $n+1$ Linear Equations in n Unknowns in Terms of Its Least Squares Solution

SIAM Review ◽  
1968 ◽  
Vol 10 (3) ◽  
pp. 373-375 ◽  
Author(s):  
Marcel Meicler
Keyword(s):  
Least Squares ◽  
Linear Equations ◽  
Least Squares Solution ◽  
Inconsistent System

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.

Sign in / Sign up

Export Citation Format

Share Document