engleski

Recompression of Hadamard products of tensors in Tucker format

In the last decade low-rank tensors decompositions have been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. Since tensors can be given only as the solution of some algebraic equation, it is important to develop solvers working within the compressed storage scheme. That is what this thesis is concerned with, focusing on Tucker format, one of the most commonly used low-rank representation of tensors, and Hadamard product, which features prominently in tensor-based algorithms in scientific computing and data analysis. Fast algorithms are attained by combining iterative methods, such as Lanczos method and randomized algorithms, with fast matrix-vector products that exploit the structure of Hadamard products. Algorithms are implemented in programming language Julia and a new Julia library for tensors in Tucker format is presented.

Tensors, Tucker format, Tucker decomposition, higher-order singular value decomposition (HOSVD), Hadamard products, low-rank approximation

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