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Towards tensor generalizations of TLS & core problem theory
Author(s) -
Hnětynková Iveta,
Plešinger Martin,
Žáková Jana
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800196
Subject(s) - tensor (intrinsic definition) , generalization , core (optical fiber) , context (archaeology) , algebra over a field , mathematics , matrix (chemical analysis) , computer science , algebraic number , pure mathematics , mathematical analysis , telecommunications , paleontology , materials science , composite material , biology
Despite the wide attention, there are still several not well understood parts in the theory of total least squares (TLS) formulation of linear algebraic approximation problems. In particular, in the problems with multiple (matrix) right‐hand sides one can ask about the meaning of the nongeneric solution in the context of the original data, the nonexistence of the TLS solution for the so‐called irreducible core problems, etc. In the single (vector) right‐hand side TLS, these problems can be easily explained through the core problem theory or simply do not appear. Here we summarize, how the existing TLS and core problem theory can be generalized to problems with tensor right‐hand sides. Such generalization also gives a natural and wider context for further analysis of the above mentioned questions.