摘要
数学反演思想的哲学基础是辩证法的对立统一规律,不同的反演思想反映了对立统一规律中的两个对立面的不同变化形态。在讨论反演变换、级数反演、反问题理论、关系映射反演方法和反演集合理论的思想差异和相互关系的基础上指出:关系映射反演方法思想包含级数反演思想,级数反演思想包含反演变换思想,在有限集上关系映射反演方法和反问题理论可统一为反演集合理论。同时举例说明了反演集合理论在反问题理论(联合反演)中的应用。
In this thesis, the author thinks that the philosophical basis for inversion thoughts in mathematics is the law of the unity of opposites within the dialectics. The ideological differentiae and mutual relations are discussed in this thesis among the inversion transformation, the series reversion, the inverse problem theory, the method of relation mapping inversion, and the inversion set theory. The author points out that method of relation mapping inversion comprises series reversion, while series reversion includes inversion transformation, and therefore, method of relation mapping inversion and inverse problem theory could be unified into inversion set theory within finite set. The author also illustrates the applications of inversion set theory in the inverse problem theory （joint inversion）.
出处
《昆明学院学报》
2012年第5期39-45,共7页
Journal of Kunming University
关键词
辩证法
对立统一规律
反演思想
反演集合
关系映射反演方法
反演理论
级数反演
反演变换
dialectics
the law of the unity of opposites
inversion thoughts
inversion set theory
method of relation mapping inversion
inverse problem theory
series reversion
inversion transformation
