Matches in SemOpenAlex for { <https://semopenalex.org/work/W2022800586> ?p ?o ?g. }
Showing items 1 to 49 of
49
with 100 items per page.
- W2022800586 endingPage "0767b" @default.
- W2022800586 startingPage "0767b" @default.
- W2022800586 abstract "P RUSSING points out the dangers of trying to use the principal minor test for positive definite matrices as a test for a positive semidefinite matrix. Kerr agrees, but feels that modifying the principal minor test to suit the new task is too expensive computationally. He recommends using the singular value decomposition (SVD) of the matrix as a more efficient and more stable technique to evaluate definiteness. A Choleski factorization, although computationally faster, is rejected because it is not stable for a semidefinite matrix. As an indicator of computational speed, the flop count for a Choleski factorization is given as «/6, whereas the flop count for an SVD is given as 2w/3. This Comiiient suggests a different concept for this test, namely, the inertia of a matrix. The computational burden is similar to that of a Choleski factorization and software to perform this calculation is available in LINPACK. The inertia of a symmetric matrix is defined as the number triple (ir9p,£]9 where ir is the number of positive eigenvalues, p is the number of negative eigenvalues, and f is the number of zero eigenvalues. For an «th-order matrix, the statement that it is positive definite is equivalent to the statement that its inertia is {n,0,0]. Similarly, a positive semidefinite matrix would have an inertia of {m,Q,p}, m+p = n. The flop count for the matrix inertia calculation is «/6, nearly four times faster than the equivalent SVD. Although the matrix inertia calculation does not indicate the magnitude of the matrix eigenvalues, it can be used to discover eigenvalue bounds (see Slicing the Spectrum in Ref. 5 for a lucid commentary). In summary, using LINPACK software to calculate the inertia of a matrix is a computationally efficient way to check whether the matrix is positive definite, positive semidefinite, or indefinite. The SVD is more suitable if information on why the matrix is not positive definite is required." @default.
- W2022800586 created "2016-06-24" @default.
- W2022800586 creator A5085224143 @default.
- W2022800586 date "1989-09-01" @default.
- W2022800586 modified "2023-09-24" @default.
- W2022800586 title "Reply by Author to J. L. Tietze" @default.
- W2022800586 cites W133977063 @default.
- W2022800586 cites W2075610771 @default.
- W2022800586 cites W2103679894 @default.
- W2022800586 doi "https://doi.org/10.2514/3.56497" @default.
- W2022800586 hasPublicationYear "1989" @default.
- W2022800586 type Work @default.
- W2022800586 sameAs 2022800586 @default.
- W2022800586 citedByCount "1" @default.
- W2022800586 crossrefType "journal-article" @default.
- W2022800586 hasAuthorship W2022800586A5085224143 @default.
- W2022800586 hasConcept C138885662 @default.
- W2022800586 hasConcept C199343813 @default.
- W2022800586 hasConcept C2777686260 @default.
- W2022800586 hasConcept C33923547 @default.
- W2022800586 hasConcept C41008148 @default.
- W2022800586 hasConcept C71924100 @default.
- W2022800586 hasConceptScore W2022800586C138885662 @default.
- W2022800586 hasConceptScore W2022800586C199343813 @default.
- W2022800586 hasConceptScore W2022800586C2777686260 @default.
- W2022800586 hasConceptScore W2022800586C33923547 @default.
- W2022800586 hasConceptScore W2022800586C41008148 @default.
- W2022800586 hasConceptScore W2022800586C71924100 @default.
- W2022800586 hasIssue "5" @default.
- W2022800586 hasLocation W20228005861 @default.
- W2022800586 hasOpenAccess W2022800586 @default.
- W2022800586 hasPrimaryLocation W20228005861 @default.
- W2022800586 hasRelatedWork W1979597421 @default.
- W2022800586 hasRelatedWork W2007980826 @default.
- W2022800586 hasRelatedWork W2061531152 @default.
- W2022800586 hasRelatedWork W2063488590 @default.
- W2022800586 hasRelatedWork W2748952813 @default.
- W2022800586 hasRelatedWork W2899084033 @default.
- W2022800586 hasRelatedWork W3002753104 @default.
- W2022800586 hasRelatedWork W4225152035 @default.
- W2022800586 hasRelatedWork W4230623537 @default.
- W2022800586 hasRelatedWork W4245490552 @default.
- W2022800586 hasVolume "12" @default.
- W2022800586 isParatext "false" @default.
- W2022800586 isRetracted "false" @default.
- W2022800586 magId "2022800586" @default.
- W2022800586 workType "article" @default.