zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix. (English) Zbl 1153.65030
An order $n$ algorithm is given to compute the elements of the inverse of an $n\times n$ tridiagonal ($m=3$) or a pentadiagonal ($m=5$) matrix. It is based on an $m$-term vector recurrence for the columns of the inverse matrix. This recurrence computes the successive columns of the inverse essentially starting from the last one ($m=3$) or from the last two columns ($m=5$). The elements of these initializing vectors for the recurrence are themselves computed by a scalar $m$-term recurrence.

65F05Direct methods for linear systems and matrix inversion (numerical linear algebra)
65F50Sparse matrices (numerical linear algebra)
65F40Determinants (numerical linear algebra)
Full Text: DOI
[1] Hadj, D. Aiat; Elouafi, M.: On the characteristic polynomial, eigenvectors and determinant of a pentadiagonal matrix. Appl. math. Comput. 198, No. 2, 634-642 (2008) · Zbl 1138.65034
[2] El-Mikkawy, M.; Karawia, A.: Inversion of general tridiagonal matrices. Appl. math. Lett. 19, 712-720 (2006) · Zbl 1119.65022
[3] Mallik, Ranjan K.: The inverse of a tridiagonal matrix. Linear algebra appl. 325, No. 1 -- 3, 109-139 (2001) · Zbl 0980.15004
[4] Kilic, Emrah: Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions. Appl. math. Comput. 197, No. 1, 345-357 (2008) · Zbl 1151.65021
[5] Losiak, Janina; Neuman, E.; Nowak, Jolanta: The inversion of cyclic tridiagonal matrices. Zastos. mat. 20, No. 1, 93-102 (1988) · Zbl 0697.65018