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On the inversion of certain band matrices

100%

Neuman E.

Mathematica Applicanda

1977

tom 5

nr 9

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

Eigenvalue problems with indefinite weight

100%

Szulkin A., Willem M.

Studia Mathematica

1999

tom 135

nr 2

191-201

We consider the linear eigenvalue problem -Δu = λV(x)u, $u ∈ D^{1,2}_0(Ω)$, and its nonlinear generalization $-Δ_{p}u = λV(x)|u|^{p-2}u$, $u ∈ D^{1,p}_0(Ω)$. The set Ω need not be bounded, in particular, $Ω = ℝ^N$ is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues $λ_n → ∞$.

Ograniczanie wyników

1 Mathematica Applicanda

1 Studia Mathematica

1 Neuman E.

1 Szulkin A.

1 Willem M.

1 1999

1 1977

Wyniki wyszukiwania

On the inversion of certain band matrices

Eigenvalue problems with indefinite weight