[PDF] $$\mathcal O(n)$$O(n) working precision inverses for symmetric tridiagonal Toeplitz matrices with $$\mathcal O(1)$$O(1) floating point calculations | Semantic Scholar

A well known numerical task is the inversion of large symmetric tridiagonal Toeplitz matrices, i.e., matrices whose entries equal a on the diagonal and b on the extra diagonals ($$a, b\in \mathbb R$$a,b∈R). The inverses of such matrices are dense and there exist well known explicit formulas by which they can be calculated in $$\mathcal O(n^2)$$O(n2). In this note we present a simplification of the problem that has proven to be rather useful in everyday practice: If $$\vert a\vert > 2\vert b… Expand

It is shown that the piecewise linear equation system, based on the jats:inline-formula, can be implemented as a discrete-time solution to the inequality problem.Expand

This work has developed a direct method of solution involving Fourier analysis which can solve Poisson''s equation in a square region covered by a 48 x 48 mesh in 0.9 seconds on the IBM 7090.Expand