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IMA Journal of Numerical Analysis Advance Access published online on July 2, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn076
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Numerical approximations to the mass transfer problem on compact spaces

J. Rigoberto Gabriel{dagger}

Facultad de Matemáticas, Universidad Veracruzana, A. Postal 270, Xalapa, Veracruz 91090, México

Juan González-Hernández{ddagger}

Departamento de Probabilidad y Estadística, IIMAS-UNAM, A. Postal 20-726, México D.F. 01000, México

Raquiel R. López-Martínez§

Facultad de Matemáticas, Universidad Veracruzana, A. Postal 270, Xalapa, Veracruz 91090, México

{dagger} Corresponding author. Email: jgabriel{at}uv.mx

{ddagger} Email: juan{at}sigma.iimas.unam.mx

§ Email: ralopez{at}uv.mx

Received on 6 December 2007. Revised on 6 October 2008.


  Abstract

This paper presents a numerical approximation for the value of the Monge–Kantorovich mass transfer (MT) problem on compact metric spaces. A sequence of transportation problems is built and it is proven that the value of the MT problem is the limit of the optimal values of these problems. Moreover, we give an error bound for the numerical approximation. A couple of illustrative computational examples are presented.

Key Words: mass transfer problem; approximation scheme; finite-dimensional linear program


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