數(shù)值分析

第1章  數(shù)的表示. 浮點算術和數(shù)值算法的誤差                  
     1.1  數(shù)的表示和誤差                  
          1.1.1  整數(shù)的機內表示和范圍                  
          1.1.2  浮點數(shù)的機內表示和范圍                  
          1.1.3  相對誤差. 絕對誤差和精度                  
     1.2  浮點算術                  
      1.2.1  浮點四則運算的舍入誤差分析                  
      1.2.2  常用浮點運算的舍入誤差分析                  
 1.3  算法復雜性和數(shù)值算法的誤差                  
      1.3.1  什么是算法                  
      1.3.2  算法的計算復雜性                  
      1.3.3  向后誤差分析和算法的數(shù)值穩(wěn)定性                  
          1.3.4  算法的評價標準                  
 本章小結                  
 習題一                  
 第2章  函數(shù)方程求根                  
 2.1  兩分法                  
 2.2  迭代法                  
      2.2.1  迭代法的基本思想                  
      2.2.2  迭代過程的收斂性                  
      2.2.3  迭代過程的收斂速度                  
      2.3  Newton法                  
      2.4  弦截法                  
 本章小結                  
 習題二                  
 第3章  線性代數(shù)方程組求解                  
 3.1  向量和矩陣的范數(shù)以及誤差分析                  
      3.1.1  向量的范數(shù)                  
      3.1.2  矩陣的范數(shù)                  
      3.1.3  矩陣的條件數(shù)和誤差分析                  
 3.2  解線性代數(shù)方程組的直接法                  
      3.2.1  Jordan消去法                  
      3.2.2  Gauss消去法                  
      3.2.3  選主元的Gauss消去法                  
      3.2.4  對角元為主元的充分條件                  
      3.2.5  追趕法                  
      3.2.6  平方根法                  
 3.3  迭代法                  
      3.3.1  迭代格式的建立                  
      3.3.2  迭代過程的收斂性                  
      3.3.3  直接法的迭代改善                  
 本章小結                  
 習題三                  
 第4章  插值與逼近                  
 4.1  線性插值和拋物插值                  
 4.2  Lagrange插值                  
 4.3  Aitken算法和代數(shù)插值的Runge(龍格)現(xiàn)象                  
      4.3.1  Aitken逐步線性插值                  
      4.3.2  高次插值的Runge現(xiàn)象                  
 4.4  樣條插值                  
 4.5  曲線擬合的最小二乘法                  
      4.5.1  線性擬合                  
      4.5.2  多項式擬合                  
      4.5.3  解最小二乘問題的正交三角化方法                  
 4.6  函數(shù)逼近                  
      4.6.1  最佳一致逼近                  
      4.6.2  最佳平方逼近                  
 本章小結                  
 習題四                  
 第5章  數(shù)值積分                  
 5.1  求積公式和它的代數(shù)精度                  
     5.1.1  基本公式                  
     5.1.2  復化公式                  
     5.1.3  插值型求積公式                  
 5.2  Romberg求積算法                  
     5.2.1  變步長梯形求積法                  
     5.2.2  Romberg公式                  
 5.3  利用樣條插值的求積公式                  
 本章小結                  
 習題五                  
 第6章  常微分方程的數(shù)值解法                  
 6.1  數(shù)值解法的基本思想與途徑                  
     6.1.1  數(shù)值解法的必要性                  
     6.1.2  數(shù)值方法的基本思想                  
     6.1.3數(shù)值解法的基本途徑                  
 6.2  Euler(歐拉)方法                  
     6.2.1  三個基本公式                  
     6.2.2  基本公式的誤差分析                  
     6.2.3  預估(預測)校正公式(改進的Euler公式)                  
 6.3  RungeKutta法                  
     6.3.1  RungeKutta法的基本思想                  
     6.3.2  三階RungeKutta法                  
     6.3.3  四階RungeKutta法                  
     6.3.4  變步長的RungeKutta法                  
 6.4 線性多步法                  
     6.4.1 Adams(阿達姆斯)方法                  
     6.4.2 Adams預估校正公式                  
 6.5 收斂性和穩(wěn)定性                  
     6.5.1 收斂性                  
     6.5.2 穩(wěn)定性                  
 6.6 方程組和高階方程的情形                  
     6.6.1 一階方程組                  
     6.6.2 化高階方程為一階方程組                  
 6.7 邊值問題                  
 本章小結                  
 習題六                  
 第7章 FFT及其應用                  
 7.1 離散Fourier變換                  
     7.1.1 一維Fourier變換                  
     7.1.2 高維變換                  
 7.2 快速Fourier變換及其實現(xiàn)                  
     7.2.1 FFT思想                  
     7.2.2 FFT算法框架                  
     7.2.3 穩(wěn)定性結果                  
 7.3 離散余弦變換                  
     7.3.1 DCT變換的8種形式                  
     7.3.2 快速DCT變換                  
     7.3.3 DCT變換在JPEG標準中的應用                  
 本章小結                  
 習題七                  
 第8章 并行計算初步                  
 8.1 并行基礎                  
     8.1.1 為什么要并行                  
     8.1.2 并行計算系統(tǒng)                  
     8.1.3 發(fā)展趨勢                  
 8.2 程序設計基礎                  
     8.2.1 分布式內存系統(tǒng)                  
     8.2.2 共享式內存系統(tǒng)                  
 8.3 軟件平臺                  
     8.3.1 PVM平臺                  
     8.3.2 MPI平臺                  
 8.4 ScaLAPACK簡介                  
     8.4.1 ScaLAPACK的結構                  
     8.4.2 ScaLAPACK的安裝                  
     8.4.3 ScaLAPACK的過程說明                  
     8.4.4 一個ScaLAPACK例子                  
 本章小結                  
 習題八                  
 主要參考文獻