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[Windows Develop] problem9 DL : 0: Description 给定n个输入输出对，用给定的m次多项式拟合输入输出关系。当n大于多项式阶数m时，化为超定方程求解问题。这里采用最小二乘方法求解。问题建模如下： 1 化为矩阵形式： 2 其中 3 对上式求导，易得 4 利用对X的QR分解可以有效地降低上述运算的复杂度，并提高精度。请完成推导，并据此设计算法计算参数a*。 Input Description 第一行输入n和m。此后每行依次输入一组。均为浮点数。 Output Description 将计算得到的多项式参数由低阶到高阶逐行输出。只需保留整数部分。-Description Given n input-output pairs, with a given m-order polynomial fitting the input-output relationship. When n is greater than the polynomial order m, into overdetermined equations to solve the problem. Using the least squares method to solve here. MODELING as follows: 1 into a matrix form: 2 wherein Formula seek three pairs of the guide, and easy to get 4 X' s use of QR decomposition can effectively reduce the arithmetic complexity, and improve accuracy. Please complete derivation, and accordingly design algorithm parameters a*. Input Description The first line of input n and m. Then every line in turn enter a group. They are floating point numbers. Output Description The polynomial parameters calculated by the low-level to high-end progressive output. Simply reserved integer part.
Date : 2025-12-30 Size : 1kb User : mingren