The family of cubic Thue equation which depend on two parameters ｜ x^3 ＋ mx^2 y-（m＋3） xy^2＋y^3｜=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is...The family of cubic Thue equation which depend on two parameters ｜ x^3 ＋ mx^2 y-（m＋3） xy^2＋y^3｜=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is quite better than the present result. Moreover, we study two inequalities ｜ x^3 ＋ mx^2y-（m ＋ 3） xy^2＋y^3 ｜ =k≤2m＋3 and ｜x^3 ＋mx^2y- （m＋3）xy^2 ＋ y^3｜ = k≤ （2m＋3）^2 separately. Our result of upper bound make it easy to solve those inequalities by simple method of continuous fraction expansion.展开更多
A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Til...A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Tile matrix quotients are based oil the generalized inverse for a matrix, Which is found to beeffective in continued fraction interpolation. In this paper, tWo dual expansions for bivariate matrix valuedThiele-type interpolating continued fractions are presented, then, tWo dual rational interpolants are definedout of them.展开更多
基金Supported by the National Natural ScienceFoundation of China (2001AA141010)
文摘The family of cubic Thue equation which depend on two parameters ｜ x^3 ＋ mx^2 y-（m＋3） xy^2＋y^3｜=k is studied. Using rational approximation, we give a smaller upper bound of the solution of the equation, that is quite better than the present result. Moreover, we study two inequalities ｜ x^3 ＋ mx^2y-（m ＋ 3） xy^2＋y^3 ｜ =k≤2m＋3 and ｜x^3 ＋mx^2y- （m＋3）xy^2 ＋ y^3｜ = k≤ （2m＋3）^2 separately. Our result of upper bound make it easy to solve those inequalities by simple method of continuous fraction expansion.
文摘A new method for the construction of bivariate matrix valued rational interpolants on a rectangulargrid is introduced. The rational interpolants are expressed in the continued fraction form with scalardenominator. Tile matrix quotients are based oil the generalized inverse for a matrix, Which is found to beeffective in continued fraction interpolation. In this paper, tWo dual expansions for bivariate matrix valuedThiele-type interpolating continued fractions are presented, then, tWo dual rational interpolants are definedout of them.
