A Representation of Nonhomogeneous Quadratic Forms with Application to the Least Squares Solution | Zendy

Czesław Stępniak | Zendy

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

Author(s) -

Czesław Stępniak

Publication year - 2011

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/385870

Subject(s) - least squares function approximation , mathematics , quadratic equation , representation (politics) , linear least squares , algebraic number , differential (mechanical device) , total least squares , generalized least squares , calculus (dental) , algebra over a field , mathematical analysis , pure mathematics , linear model , algorithm , statistics , law , engineering , geometry , medicine , dentistry , estimator , politics , political science , aerospace engineering , singular value decomposition

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

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