A new method for structured representation of matrices and vectors is presented. The method is based on the representation of a matrix as a d-dimensional tensor and applying the TT-decomposition proposed recently. It turned out that for many important cases the number of parameters to represent an n x n matrix falls down to O(log(alpha) n), giving a logarithmic storage. It is shown that this format can be used not only for storage reduction, but also for linear algebra operations. Possible applications include differential and integral equations, and data and image compression.
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机译：提出了一种矩阵和向量结构化表示的新方法。该方法基于将矩阵表示为d维张量，并应用了最近提出的TT分解。结果表明，在许多重要情况下，代表n x n矩阵的参数数量下降到O（logαn），从而得到对数存储。结果表明，这种格式不仅可以用于减少存储量，而且可以用于线性代数运算。可能的应用包括微分方程和积分方程，以及数据和图像压缩。
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