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    高師機構典藏 NKNUIR > 理學院 > 數學系 > 博碩士論文 >  Item 987654321/18659
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    題名: Gram-Schmidt數值解的探討
    Numerical study of Gram-Schmidt algorithms
    Authors: 陳如玨
    貢獻者: 陳振遠
    Jen-Yuan Chen
    Date: 2012-08-10
    Issue Date: 2013-04-19 11:49:09 (UTC+8)
    Abstract: Gram-Schmidt正交化已有相當一段歷史,一般教科書上會提到古典Gram-Schmidt正交化方法,但從計算觀點,該方法會出現正交後的向量不能完全正交的情況。修正後的Gram-Schmidt正交方法,可以改善這些問題,而Householder正交方法比這兩種來的更好。最近提出的兩步驟正交化方法,可以比的上Householder的方法。本論文就這四種方法做一些數值上的比較。
    The Gram-Schmidt orthogonalization (cgs) has been known for a long time. Many textbooks mention this method. However, in floating point arithmetic, cgs may produce a set of vectors that are far from orthogonal. For modified Gram-Schmidt orthogonalization, it may produce a more orthogonal set of vectors. The Householder orthogonalization can produce more orthogonal vectors than those of cgs and mgs. Recently, Two-step classical Gram-Schmidt orthogonalization has been proposed which is competitive to Householder method. We will compare these four methods by numerical results.
    Appears in Collections:[數學系] 博碩士論文
    [數學系] 陳振遠

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