BERMAN M, SHAHN E, WEISS M F
Biophys J. 1962 May;2(3):275-87. doi: 10.1016/s0006-3495(62)86855-6.
A mathematical formalism is presented for use with digital computers to permit the routine fitting of data to physical and mathematical models. Given a set of data, the mathematical equations describing a model, initial conditions for an experiment, and initial estimates for the values of model parameters, the computer program automatically proceeds to obtain a least squares fit of the data by an iterative adjustment of the values of the parameters. When the experimental measures are linear combinations of functions, the linear coefficients for a least squares fit may also be calculated. The values of both the parameters of the model and the coefficients for the sum of functions may be unknown independent variables, unknown dependent variables, or known constants. In the case of dependence, only linear dependencies are provided for in routine use. The computer program includes a number of subroutines, each one of which performs a special task. This permits flexibility in choosing various types of solutions and procedures. One subroutine, for example, handles linear differential equations, another, special non-linear functions, etc. The use of analytic or numerical solutions of equations is possible.
提出了一种与数字计算机配合使用的数学形式体系，以便将数据常规拟合到物理模型和数学模型。给定一组数据、描述模型的数学方程、实验的初始条件以及模型参数值的初始估计值，计算机程序会通过对参数值进行迭代调整，自动进行数据的最小二乘拟合。当实验测量值是函数的线性组合时，也可以计算最小二乘拟合的线性系数。模型参数值和函数和的系数既可以是未知自变量、未知因变量，也可以是已知常数。在依赖关系的情况下，常规使用中仅提供线性依赖关系。该计算机程序包括多个子程序，每个子程序执行一项特殊任务。这使得在选择各种类型的解决方案和程序时具有灵活性。例如，一个子程序处理线性微分方程，另一个处理特殊的非线性函数等。方程的解析解或数值解都可以使用。
