第四章解線性方程組的迭代法(編輯修改稿)
2025-08-19 10:21 本頁面
【文章內(nèi)容簡(jiǎn)介】 1( ???? AAA （ 正定性 /* positive definite */ ) ||||||||||)2( AA ?? ?? C??對(duì)任意 (齊次性 /* homogeneous */ ) ||||||||||||)3( BABA ??? （ 三角不等式 /* triangle inequality */ ) (4)* || AB || ? || A || || B || （ 相容 /* consistent */ 當(dāng) m = n 時(shí) ) In general, if we have || AB ||? ? || A ||? || B ||? , then the 3 norms are said to be consistent. Oh haven’ t I had enough of new concepts? What do I need the consistency for? When you have to analyze the error bound of AB – imagine you doing it without a consistent matrix norm… 167。 1 Norms of Vectors and Matrices – Matrix Norms 常用矩陣范數(shù)： Frobenius 范數(shù) ? ?? ??ninjijF aA1 12|||||| — 向量 || ||2的直接推廣 對(duì)方陣 以及 有 nnRA ?? nRx??22 |||||||||||| xAxA F ?? ??利用 Cauchy 不等式 可證。 22 |||||||||| yxyx ???? ???算子范數(shù) /* operator norm */ 由向
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