Bidiagonal
E440653
Bidiagonal is a special kind of sparse matrix that has nonzero entries only on the main diagonal and either the superdiagonal or subdiagonal, making it efficient for numerical linear algebra computations.
Observed surface forms (4)
| Surface form | Occurrences |
|---|---|
| Bidiagonal matrix | 0 |
| Lower bidiagonal matrix | 0 |
| Upper bidiagonal matrix | 0 |
| Golub–Kahan bidiagonalization | 1 |
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
Bidiagonal matrix
ⓘ
Bidiagonal matrix ⓘ Matrix type ⓘ Sparse matrix ⓘ |
| belongsTo | Linear algebra ⓘ |
| enables |
Fast matrix–vector multiplication
ⓘ
Reduced storage requirements ⓘ |
| hasApplicationIn |
Computational physics
ⓘ
Data analysis ⓘ Numerical analysis ⓘ Scientific computing ⓘ |
| hasComplexityForMatVec | O(n) ⓘ |
| hasNonzeroEntriesOn |
Main diagonal
ⓘ
Subdiagonal ⓘ Superdiagonal ⓘ Superdiagonal or subdiagonal ⓘ |
| hasProperty |
At most two nonzero diagonals
ⓘ
Band matrix with bandwidth 1 ⓘ Structured sparsity pattern ⓘ |
| hasStorageComplexity | O(n) ⓘ |
| hasVariant |
Lower bidiagonal matrix
ⓘ
Upper bidiagonal matrix ⓘ |
| isCharacterizedBy | Nonzeros confined to two adjacent diagonals ⓘ |
| isContrastedWith |
Dense matrix
ⓘ
Diagonal matrix ⓘ Tridiagonal matrix ⓘ |
| isDefinedOver | Real numbers or complex numbers ⓘ |
| isObtainedBy | Bidiagonalization process ⓘ |
| isObtainedFrom | General matrix ⓘ |
| isSpecialCaseOf |
Band matrix
ⓘ
Sparse matrix ⓘ Tridiagonal matrix ⓘ |
| isUsedFor |
Efficient matrix computations
ⓘ
Eigenvalue algorithms ⓘ Singular value decomposition NERFINISHED ⓘ |
| isUsedIn |
Golub–Kahan SVD algorithm
NERFINISHED
ⓘ
Iterative methods for linear systems ⓘ Least squares computations ⓘ Numerical linear algebra ⓘ Orthogonal transformations ⓘ QR algorithm ⓘ |
| isUsedWith |
Givens rotations
NERFINISHED
ⓘ
Householder reflections NERFINISHED ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Golub–Kahan bidiagonalization