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- Bidiagonalization abstract "Bidiagonalization is one of unitary (orthogonal) matrix decompositions such that U* A V = B, where U and V are unitary (orthogonal) matrices; * denotes Hermitian transpose; and B is upper bidiagonal. A is allowed to be rectangular.For dense matrices, the left and right unitary matrices are obtained by a series of Householder reflections alternately applied from the left and right. This is known as Golub-Kahan bidiagonalization. For large matrices, they are calculated iteratively by using Lanczos method, referred to as Golub-Kahan-Lanczos method.Bidiagonalization has a very similar structure to the singular value decomposition (SVD). However, it is computed within finite operations, while SVD requires iterative schemes to find singular values. It is because the squared singular values are the roots of characteristic polynomials of A* A, where A is assumed to be tall.".
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- Bidiagonalization wikiPageRevisionID "615914619".
- Bidiagonalization wikiPageWikiLink Bidiagonal_matrix.
- Bidiagonalization wikiPageWikiLink Category:Matrix_theory.
- Bidiagonalization wikiPageWikiLink Category:Numerical_linear_algebra.
- Bidiagonalization wikiPageWikiLink Characteristic_polynomial.
- Bidiagonalization wikiPageWikiLink Conjugate_transpose.
- Bidiagonalization wikiPageWikiLink Dense_matrix.
- Bidiagonalization wikiPageWikiLink Hermitian_transpose.
- Bidiagonalization wikiPageWikiLink Householder_reflection.
- Bidiagonalization wikiPageWikiLink Householder_transformation.
- Bidiagonalization wikiPageWikiLink Lanczos_algorithm.
- Bidiagonalization wikiPageWikiLink Matrix_decomposition.
- Bidiagonalization wikiPageWikiLink Orthogonal_matrix.
- Bidiagonalization wikiPageWikiLink Singular_value_decomposition.
- Bidiagonalization wikiPageWikiLink Sparse_matrix.
- Bidiagonalization wikiPageWikiLink Unitary_matrix.
- Bidiagonalization wikiPageWikiLinkText "Bidiagonalization".
- Bidiagonalization wikiPageWikiLinkText "bidiagonalization".
- Bidiagonalization hasPhotoCollection Bidiagonalization.
- Bidiagonalization wikiPageUsesTemplate Template:Citation.
- Bidiagonalization wikiPageUsesTemplate Template:Numerical_linear_algebra.
- Bidiagonalization subject Category:Matrix_theory.
- Bidiagonalization subject Category:Numerical_linear_algebra.
- Bidiagonalization type Article.
- Bidiagonalization type Article.
- Bidiagonalization comment "Bidiagonalization is one of unitary (orthogonal) matrix decompositions such that U* A V = B, where U and V are unitary (orthogonal) matrices; * denotes Hermitian transpose; and B is upper bidiagonal. A is allowed to be rectangular.For dense matrices, the left and right unitary matrices are obtained by a series of Householder reflections alternately applied from the left and right. This is known as Golub-Kahan bidiagonalization.".
- Bidiagonalization label "Bidiagonalization".
- Bidiagonalization sameAs m.0dp93l.
- Bidiagonalization sameAs Q4904167.
- Bidiagonalization sameAs Q4904167.
- Bidiagonalization wasDerivedFrom Bidiagonalization?oldid=615914619.
- Bidiagonalization isPrimaryTopicOf Bidiagonalization.