ILL-POSED INVERSE PROBLEMS IN CHEMISTRY

被引：5

作者：

Braga, Joao P. ^{[1
]}

Lemes, Nelson H. T. ^{[2
]}

Borges, Emilio ^{[3
]}

Sebastiao, Rita C. O. ^{[1
]}

机构：

[1] Univ Fed Minas Gerais, Dept Quim, BR-31270901 Belo Horizonte, MG, Brazil

[2] Univ Fed Alfenas, Dept Quim, BR-37130000 Alfenas, MG, Brazil

[3] Univ Fed Vicosa, Dept Quim, BR-36570900 Vicosa, MG, Brazil

来源：

QUIMICA NOVA | 2016年 / 39卷 / 07期

关键词：

inverse problem; ill-posed problem; regularization; Hopfield neural network; POTENTIAL-ENERGY FUNCTION; SINGULAR-VALUE DECOMPOSITION; 2ND VIRIAL-COEFFICIENTS; NEURAL-NETWORK; TIKHONOV REGULARIZATION;

D O I：

10.5935/0100-4042.20160104

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

What is an ill-posed inverse problem? The answer to this question is the main objective of the present paper and the pre-requisite to follow the material requires only elementary calculus. The first mathematical formulation of an inverse problem, due to N. H. Abel, together with the fundamental work by Jacques Hadamard, are explored at the beginning of the paper. A prototype system is used to consider the regularization concept. Three numerical methods, the Tikhonov regularization, the decomposition into singular values and the Hopfield neural networks, applied to remove the singularity are examined. General aspects of the ill-posed inverse problems in chemistry with emphasis in thermodynamics and a set of general rules for other areas of science are also analyzed.

引用

页码：886 / 891

页数：6

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