Descr iption





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 Descr iption



第一行输入n和m。此后每行依次输入一组 。均为浮点数。



Output Descr iption



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。-Descr iption 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 Descr iption The first line of input n and m. Then every line in turn enter a group. They are floating point numbers. Output Descr iption The polynomial parameters calculated by the low-level to high-end progressive output. Simply reserved integer part.