凌波初步 第一章 勘誤

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$\phi(x)$ 是不連續函數，$\cdots$

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\begin{displaymath}\sum_{k=0}^{2^j-1} v_{jk}\phi(2^jx-k),\quad \cdots \end{displaymath}

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\begin{displaymath}\cdots\quad v(x)=\sum_{k=0}^{2^j-1}\quad\cdots \eqno(1.14) \end{displaymath}

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$\cdots$ 前面的結論再綜合一遍：

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\begin{displaymath}\cdots \mathcal{P}_jf(x) + w_{jk}\times\cases{1 & $\cdots$\cr -1& $\cdots$}\eqno(1.30) \end{displaymath}

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\begin{displaymath}\cdots \mathcal{P}_jf(x) + {w_{jk}\over\sqrt{2^j}}\psi_{jk}(x), \cdots \end{displaymath}

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\begin{eqnarray*}&\displaystyle\cdots = \frac{v_{j+1,2k}}{\sqrt{2^{j+1}}}\phi_{j... ...hi_{jk}(x) + {w_{jk}\over\sqrt{2^j}}\psi_{jk}(x) &\qquad (1.33) \end{eqnarray*}


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\begin{displaymath}\phi_{00}, \psi_{00}, \psi_{10}, \psi_{11}, \cdots \end{displaymath}

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\begin{eqnarray*}&\displaystyle =\sum_{k=0}^{2^\ell-1} {v_k\over\sqrt{2^\ell}}\p... ...e =\cdots \sum_{k=0}^{2^j-1} {w_{jk}\over\sqrt{2^j}}\psi_{jk}(x) \end{eqnarray*}


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\begin{displaymath}\cdots\pmatrix{v_0\cr v_1\cr v_2\cr v_3\cr\vdots\cr v_{N-1}}_{N\times 1} \end{displaymath}

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${\cal W}^{-1}$ 的係數。

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$\cdots$ 需要 4 flops，$\cdots$

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\begin{eqnarray*}&p_0v_{2k} + q_0v_{2k+1} \mapsto \hbox{\tt tmp} \\ &p_1v_{2k} + q_1v_{2k+1} \mapsto v_{2k+1} \\ &\hbox{\tt tmp} \mapsto v_{2k} \end{eqnarray*}


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(回顧 p0=p1=1，q0=1，q1=-1。)$\cdots$

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$\cdots$ 注意 wj 的元素個數就是 2j。$\cdots$

Created: Mar 23, 1999
Last Revised: Mar 23, 1999
© Copyright 1999 Wei-Chang Shann

shann@math.ncu.edu.tw