6533b870fe1ef96bd12cfccc
RESEARCH PRODUCT
Normalizing biproportional methods
Louis De Mesnardsubject
JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C67 - Input–Output Modelsjel:C63Diagonaljel:C67JEL: D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D57 - Input–Output Tables and Analysismathematical economicsColumn (database)Projection (linear algebra)Combinatoricssymbols.namesakeMatrix (mathematics)JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C63 - Computational Techniques • Simulation ModelingmatricesJEL : D - Microeconomics/D.D5 - General Equilibrium and Disequilibrium/D.D5.D57 - Input–Output Tables and Analysis[ SHS.ECO ] Humanities and Social Sciences/Economies and financesNon negativity[SHS.ECO] Humanities and Social Sciences/Economics and FinanceGeneral Environmental ScienceMathematicsJEL : C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C67 - Input–Output ModelsGeneral Social Sciences[SHS.ECO]Humanities and Social Sciences/Economics and Financejel:D57community developmentJEL : C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C63 - Computational Techniques • Simulation ModelingLagrange multiplierPath (graph theory)symbolsdescription
International audience; Biproportional methods are used to update matrices: the projection of a matrix Z to give it the column and row sums of another matrix is R Z S, where R and S are diagonal and secure the constraints of the problem (R and S have no signification at all because they are not identified). However, normalizing R or S generates important mathematical difficulties: it amounts to put constraints on Lagrange multipliers, non negativity (and so the existence of the solution) is not guaranteed at equilibrium or along the path to equilibrium.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-02-01 |