Abstract
When the overdetermined system of linear equations $$AX \approx B$$ ((1)) has no solution, compatibility may be restored by an orthogonal projection method to estimate the relationship between A and B, where we assume A ∈ ℜm×n has numerical rank k and B ∈ ℜm×n (m ≥ n + d). The least squares (LS) and total least squares (TLS) are two common orthogonal projection methods used to solve (1). The idea is to determine an orthogonal projection matrix P by some method M such that [Ã, B̃]=P[A, B], ÃX≈ B̃ is compatible, and rank(Ã) = k. Denote by X m the minimum norm solution to ÃX≈ B̃ by method M. Let (math) be an orthonormal matrix such that ∥[A, B]∥≈ small and [Ã, B̃]=0.KeywordsSingular Value DecompositionTotal Little SquarePerturbation BoundOverdetermined SystemMinimum Norm SolutionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
