On the inversion of certain band matrices

E. Neuman. "On the inversion of certain band matrices." Mathematica Applicanda 5.9 (1977): null. <http://eudml.org/doc/293048>.

@article{E1977,
abstract = {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},
author = {E. Neuman},
journal = {Mathematica Applicanda},
keywords = {spline interpolation; matrix invers; eigenvalue problem},
language = {eng},
number = {9},
pages = {null},
title = {On the inversion of certain band matrices},
url = {http://eudml.org/doc/293048},
volume = {5},
year = {1977},
}

TY - JOUR
AU - E. Neuman
TI - On the inversion of certain band matrices
JO - Mathematica Applicanda
PY - 1977
VL - 5
IS - 9
SP - null
AB - 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
LA - eng
KW - spline interpolation; matrix invers; eigenvalue problem
UR - http://eudml.org/doc/293048
ER -