Tensor ranks for the inversion of tensor-product binomials
The main result reads: if a nonsingular matrix A of order n = p q is a tensor-product binomial with two factors then the tensor rank of A − 1 is bounded from above by min { p , q } . The estimate is sharp, and in the worst case it amounts to n .
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| Veröffentlicht in: | Journal of computational and applied mathematics 2010-10, Vol.234 (11), p.3170-3174 |
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| container_end_page | 3174 |
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| container_issue | 11 |
| container_start_page | 3170 |
| container_title | Journal of computational and applied mathematics |
| container_volume | 234 |
| creator | Tyrtyshnikov, Eugene |
| description | The main result reads: if a nonsingular matrix
A
of order
n
=
p
q
is a tensor-product binomial with two factors then the tensor rank of
A
−
1
is bounded from above by
min
{
p
,
q
}
. The estimate is sharp, and in the worst case it amounts to
n
. |
| doi_str_mv | 10.1016/j.cam.2010.02.006 |
| format | Article |
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A
of order
n
=
p
q
is a tensor-product binomial with two factors then the tensor rank of
A
−
1
is bounded from above by
min
{
p
,
q
}
. The estimate is sharp, and in the worst case it amounts to
n
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A
of order
n
=
p
q
is a tensor-product binomial with two factors then the tensor rank of
A
−
1
is bounded from above by
min
{
p
,
q
}
. The estimate is sharp, and in the worst case it amounts to
n
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A
of order
n
=
p
q
is a tensor-product binomial with two factors then the tensor rank of
A
−
1
is bounded from above by
min
{
p
,
q
}
. The estimate is sharp, and in the worst case it amounts to
n
.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2010.02.006</doi><tpages>5</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0377-0427 |
| ispartof | Journal of computational and applied mathematics, 2010-10, Vol.234 (11), p.3170-3174 |
| issn | 0377-0427 1879-1778 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_760210636 |
| source | ScienceDirect Journals (5 years ago - present); EZB-FREE-00999 freely available EZB journals |
| subjects | Binomials Computation Estimates Inverse matrices Inversions Kronecker product Low-rank matrices Mathematical analysis Mathematical models Multilevel matrices Tensor ranks Tensors Toeplitz matrices |
| title | Tensor ranks for the inversion of tensor-product binomials |
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