差分方程在计算n阶行列式中的应用

Application of Differential Equation in Calculation of N-order Determinant

目的旨在利用差分方程寻找求行列式值的新方法.方法依照差分方程的不同类型,应用分析对比研究的方法.结果探讨了利用差分方程解决了实际应用问题—计算n阶行列式,特别是那些可以用递推法计算的行列式,往往可以利用一阶、二阶常系数差分方程,能够比较方便的求出它的值.较全面、系统地讨论了这一新的方法,总结出多种适用类型,并一一给出了具体求解过程.结论运用差分方程计算行列式值的新方法是简便而有效的.

Objective This paper aims at finding a new approach to determine the value of determinant by using differential equation. Approach By using a comparative method in accordance with the different types of differential equations. Results The authors discuss how to use different equations to solving concrete problems and conclude that for some n-order determinants, especially those that can be calculated by recursion. It is easier to apply one or two order differential equations with constant coefficients to deter- mine their value. The paper discusses this method in a comprehensive and systematic way, sums up applicable types and gives concrete solutions in each case. ConcLusion It is convenient and efficient to calculate the value of determinat by using differential equations.