Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve, the system becomes a linear ordinary differential equation (ODE) with respect to a curve in the parameter space. We can evaluate the integral by solving the linear ODE numerically. This approach to evaluate numerically definite integrals is called the holonomic gradient method (HGM) and it is useful to evaluate several normalizing constants in statistics. We will discuss and compare methods to solve linear ODE's to evaluate normalizing constants.

翻译：带有 holoomic 函数参数的直线部分差分方程的全色元体系。 当我们将参数参数限制在一维曲线上时, 系统将变成参数空间曲线的线性普通差分方程( ODE ) 。 我们可以用数值解析线性ODE 来评估整体值。 这种用于评估数字确定性整体值的方法被称为 holoonomic 梯度法( HGM ), 并且可以评估统计数据中若干正常化常数。 我们将讨论和比较用来解决线性ODE 常数的方法, 以评价常数的正常化 。