Decomposition of quantics in sums of powers

Pierre Comon; B. Mourrain

doi:10.1117/12.190826

28 October 1994 Decomposition of quantics in sums of powers

Pierre Comon, B. Mourrain

Proceedings Volume 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V; (1994) https://doi.org/10.1117/12.190826
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

Symmetric tensors of order 3 and 4 arise more and more often in Signal Processing and Automatic Control, because of the recent complementary use of High-Order Statistics. However, very little special purpose tools are at disposal for manipulating such objects in engineering problems. In this paper, diagonalization issues are analyzed, with the help of the theory of homogeneous polynomials in several variables (i.e. quantics). A considerable number of results are known for binary questions, but too few for general cubs and quartics. Efficient numerical algorithms are also lacking.

Citation Download Citation

Pierre Comon and B. Mourrain "Decomposition of quantics in sums of powers", Proc. SPIE 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V, (28 October 1994); https://doi.org/10.1117/12.190826

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