Multivariate function approximation using sparse grids and High Dimensional Model Representation – a comparison

• Autorzy: Baran M.

Warianty tytułu

PL

Przybliżanie funkcji wielu zmiennych przy użyciu sieci rzadkich i High Dimensional Model Representation – porównanie

• Języki publikacji: EN

Abstrakty

EN

In many areas of science and technology, there is a need for effective procedures for approximating multivariate functions. Sparse grids and cut-HDMR (High Dimensional Model Representation) are two alternative approaches to such multivariate approximations. It is therefore interesting to compare these two methods. Numerical experiments performed in this study indicate that the sparse grid approximation is more accurate than the cut-HDMR approximation that uses a comparable number of known values of the approximated function unless the approximated function can be expressed as a sum of high order polynomials of one or two variables.

PL

W wielu obszarach nauki i technologii potrzebne są efektywne metody aproksymacji funkcji wielu zmiennych. Sieci rzadkie i cut-HDMR (High Dimensional Model Representation) są dwoma alternatywnymi podejściami do aproksymacji funkcji wielu zmiennych. Interesujące jest zatem porównanie tych dwóch metod. Eksperymenty numeryczne przeprowadzone w ramach niniejszych badań wskazują, że aproksymacja sieciami rzadkimi jest bardziej dokładna niż aproksymacja cut-HDMR wykorzystująca porównywalną liczbę znanych o ile aproksymowana funkcja nie może być wyrażona jako suma wielomianów wysokiego stopnia jednej lub dwóch zmiennych.

Słowa kluczowe

EN

sparse grids; approximation; numerical experiments; metamodelling; curse of dimensionality

PL

sieci rzadkie; aproksymacja; eksperymenty numeryczne; metamodelowanie; przekleństwa wymiarowości

• Wydawca: Wydawnictwo Politechniki Krakowskiej im. Tadeusza Kościuszki
• Czasopismo: Czasopismo Techniczne. Nauki Podstawowe
• Rocznik: 2014
• Tom: R. 111, z. 3-NP
• Strony: 97--107
• Opis fizyczny: Bibliogr. 29 poz., wz., wykr.

Twórcy

autor

Baran M.

• Institute of Teleinformatics, Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, Poland

Bibliografia

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