We present a method designed for computing solutions of infinite dimensional non linear operators $f(x) = 0$ with a tridiagonal dominant linear part. We recast the operator equation into an equivalent Newton-like equation $x = T(x) = x - Af(x)$, where $A$ is an approximate inverse of the derivative $Df(\overline x)$ at an approximate solution $\overline x$. We present rigorous computer-assisted calculations showing that $T$ is a contraction near $\overline x$, thus yielding the existence of a solution. Since $Df(\overline x)$ does not have an asymptotically diagonal dominant structure, the computation of $A$ is not straightforward. This paper provides ideas for computing $A$, and proposes a new rigorous method for proving existence of solutions of nonlinear operators with tridiagonal dominant linear part.
A class of tridiagonal operators associated to some subshifts
考虑一类由非必要伪遍历双无限序列诱导的三对角算子。仅使用初等技术，我们证明了这些运营商的数值范围包含在工会的凸包的数值域的运营商对应于常数biinfinite序列，而其他包含时，常数序列属于由给定的biinfinite序列所产生的子移位。应用S. N. Meiller-Wilde et al.和R. Hagger，它依赖于极限算子技术，我们能够提供更一般的结果，虽然需要采取封闭的数值域。
Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
VU University Amsterdam（阿姆斯特丹自由大学）；Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo（圣保罗大学数学与计算科学学院）；Université Laval, Département de Mathématiques et de Statistique（拉瓦尔大学数学与统计系）
