On solving Diophantine equations by real matrix manipulation

Author

Yamada, Manabu ; Zun, Piao Chung ; Funahashi, Yasuyuki

Author_Institution

Res. Center for Micro-Structure Devices, Nagoya Inst. of Technol., Japan

Volume

40

Issue

1

fYear

1995

fDate

1/1/1995 12:00:00 AM

Firstpage

118

Lastpage

122

Abstract

This note presents simple algorithms for obtaining the solutions of the Diophantine equation. Our methods can produce classes of all solutions with lower degree than a specified number. The previous algorithms involve some troublesome computations, e.g., the calculation of both the controllability indexes and the observability indexes or the solution of a pole assignment problem, etc. Our contribution is that our algorithm requires only basic matrix operations such as addition, subtraction, multiplication, and inversion of given real matrices. In addition, by solving simple linear equations, the class of all minimum degree solutions can be given. Therefore the computational efforts are reduced compared with previous algorithms

Keywords

computational complexity; controllability; linear systems; matrix algebra; observability; pole assignment; Diophantine equations; basic matrix operations; computational efforts; controllability indexes; observability indexes; pole assignment problem; real matrix manipulation; simple linear equations; Controllability; Differential equations; Feedback; Linear systems; Machinery; Mechanical engineering; Observability; Polynomials;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.362888

Filename

362888