论文标题
部分可观测时空混沌系统的无模型预测
Affine Iterations and Wrapping Effect: Various Approaches
论文作者
论文摘要
如果矩阵A的光谱半径少于1，则使用实际算术的形式= AX（N + 1）= AX（N） + B收敛。但是，将间隔算术替换为真实算术可能会导致这些迭代的分歧，特别是如果限制了A a的绝对值，我们将限制一个比1的范围。当初始向量x（0）和b的组件是间隔时。我们将在理论上和实验上比较通过这些不同方法计算的迭代元素的宽度：天真的迭代，基于a的QR和SVD - 因子化的方法以及Lohner的QR-Factorization方法。基于SVD因素化的方法在计算上的要求较低，并且当矩阵缩放率较差时，它的效果良好，否则它被幼稚的迭代或Lohner的方法取代。
Affine iterations of the form x(n+1) = Ax(n) + b converge, using real arithmetic, if the spectral radius of the matrix A is less than 1. However, substituting interval arithmetic to real arithmetic may lead to divergence of these iterations, in particular if the spectral radius of the absolute value of A is greater than 1. We will review different approaches to limit the overestimation of the iterates, when the components of the initial vector x(0) and b are intervals. We will compare, both theoretically and experimentally, the widths of the iterates computed by these different methods: the naive iteration, methods based on the QR-and SVD-factorization of A, and Lohner's QR-factorization method. The method based on the SVD-factorization is computationally less demanding and gives good results when the matrix is poorly scaled, it is superseded either by the naive iteration or by Lohner's method otherwise.
