Best Approximation Pair of Two Linear Varieties via an (In)Equality by   (Fan-Todd) Beesack
  The closest point of a linear variety to an external point is found by using the equality case of an Ostrowski's type inequality. This point is given in closed form as the quotient of a (formal) and a (scalar) Gram determinant. Then, the best approximation pair of points onto two linear varieties is given, as well as characterization of this pair of best approximation points. 
M. A. Facas Vicente, Fernando Martins, Cecilia Costa and Jose Vitoria
math.MG