ILL-POSED INVERSE PROBLEMS IN CHEMISTRY

Química Nova

Universidade Federal de Viçosa, Viçosa, Brazil¹  Braga, João P.¹  Universidade Federal de Alfenas, Alfenas, Brazil¹  Sebastião, Rita C. O.¹  Universidade Federal de Minas Gerais, Belo Horizonte, Brazil¹  Lemes, Nelson H. T.¹  Borges, Emílio¹ 

关键词:  inverse problem;    ill-posed problem;    regularization;    Hopfield neural network;   

DOI  :  10.5935/0100-4042.20160104

学科分类：化学（综合）

来源: Sociedade Brasileira de Quimica

【 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.

【 授权许可】

Unknown