主观几何中一组余弦定律方程的解*
Solution of Simultaneous Equations of Cosine Law Arising from Subjectivity Geometry
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摘要: 本文讨论在主观几何应用例子[1]中出现的由余弦定理建立的一组六元二次带根式的代数方程的解.应用隐函数存在定理,本文证明这组方程存在有唯一的实解.把求解问题转化为无约束非线性优化问题,可以用已知的诸法来求解.文中给出了用下降法求解的数值例子.Abstract: This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry[1].By means of the implicit function theorem,this paper proves that there exists a unique real solution of those equations.Transforming this problem into an unconstrained nonlinear optimization problem,the solution can be found by known methods.A numerical example by descent method is given.
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[1] 云天锉,主观几何初步探讨,应用数学和力学,10,8(1989),657-662. [2] 数学手册编写组,《数学手册》,高等教育出版社,北京(1979),90. [3] 夏道行等人编著,《实变函数论与泛函分析》(下册),人民教育出版社,北京(1979). -
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