On the inversion of certain band matrices

• Autorzy: E. Neuman
• Języki publikacji: EN

Abstrakty

EN

Inversion of band matrices is the simplest, direct way of computing interpolating splines. On the other hand, when studying the convergence problems, the bounds of related inverse matrices are useful. This paper contains algorithms of inversion, based on LR decomposition, of tri- and five-diagonal matrices appearing in spline fitting problems. (In this case LR decomposition is possible and unique if one of the diagonals is fixed.) For example, inversion of a tri-diagonal matrix of dimension n requires 12n(3n+5) multiplications when the proposed algorithm is used. Some upper and lower bounds for elements of the inverse matrix are also given. Under certain additional assumptions the numerical stability is proved. MR0488663

Słowa kluczowe

EN

spline interpolation; matrix invers; eigenvalue problem

• Wydawca: Polish Mathematical Society
• Czasopismo: Mathematica Applicanda
• Rocznik: 1977
• Tom: 5
• Numer: 9

Daty

wydano

1977

online

1977-12-01

Twórcy

autor

E. Neuman

Identyfikatory

DOI

10.14708/ma.v5i9.1209