An Experiment of the Orthonormalization Method with Higher Locality of Memory References for a Large Matrix of Very Slim-Shape(Application)

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  • 非常に細長い大規模行列に対する記憶参照局所性が高い正規直交化法の実験(応用)
  • 非常に細長い大規模行列に対する記憶参照局所性が高い正規直交化法の実験
  • ヒジョウ ニ ホソナガイ ダイキボ ギョウレツ ニ タイスル キオク サンショウ キョクショセイ ガ タカイ セイキ チョッコウカホウ ノ ジッケン

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Abstract

For the orthonormalization of a large matrix of very slim-shape, compared from the ordinal method such as the modified Gram-Schmidt or the Householder-QR, the classical singular value decomposition method (CSVD) with orthonormality corrections has the higher locality of memory references which reduces the amount of data transfer across the storage hierarchy between the cache and the main memory or between the main memory and the external storage device, which makes the fast computation possible. From experiments on several computer systems, in certain cases the CSVD method can be several times faster than the modified Gram-Schmidt is examined.

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