G - Physics – 06 – F
Patent
G - Physics
06
F
G06F 17/16 (2006.01) G06F 17/30 (2006.01) G06T 1/00 (2006.01)
Patent
CA 2568852
A singular value decomposition method for decomposing a singular value of a given matrix A by means of a computer. The method comprises steps of upper- double-diagonalizing the matrix A to determine an upper-double-diagonalized matrix B of the matrix A, determining a singular value .sigma. of the matrix B as the singular value of the matrix A, and determining the singular vector of the matrix A for .sigma.. The step of determining the singular vector of the matrix A includes a substep of twisted-decomposing a matrix BTB-.sigma.2I (I is a unit matrix) by using the Miura inverse transformation, the sdLVvs transformation, the rdLVvs transformation, and the Miura transformation to diagonalize the matrix BTB.
Un procEdE de dEcomposition de valeur singuliEre destinEe A dEcomposer une valeur singuliEre d'une matrice donnEe A au moyen d'un ordinateur. Le procEdE comprend les Etapes consistant A rEaliser une double diagonalisation supErieure de la matrice A afin de dEterminer une matrice B A double diagonalisation supErieure de la matrice A, dEterminer une valeur singuliEre S de la matrice B en tant que valeur singuliEre de la matrice A, ainsi que dEterminer le vecteur singulier de la matrice A pour la valeur S. L'Etape consistant A dEterminer le vecteur singulier de la matrice A inclut une sous Etape consistant A dEcomposer en spirale une matrice B<SP>T</SP>B-S?2¿I (I est une matrice unitaire) en utilisant la transformation inverse de Miura, la transformation de type sdLVvs, la transformation de type rdLVvs et la transformation de Miura afin de diagonaliser la matrice B<SP>T</SP>B.
Iwasaki Masashi
Nakamura Yoshimasa
Sakano Shinya
Japan Science And Technology Agency
Osler Hoskin & Harcourt Llp
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