Tensor Spaces and Numerical Tensor Calculus
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Beschreibung
Special numerical techniques are already needed to deal with nxn matrices for large n. Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail,
a particular tensor calculus is needed to treat such problems.
The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc.
Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc.
First monograph on this subject in the field of numerical mathematics Contains algebraic and functional analysis aspects of tensor spaces Focuses on the numerical treatment ?
Autor*in
Wolfgang Hackbusch
Themen in »Tensor Spaces and Numerical Tensor Calculus«
high-dimensional problems numerical tensor calculus tensor formats tensor spaces tensorization
Stimmen zu »Tensor Spaces and Numerical Tensor Calculus«
“The present book Tensor spaces and numerical tensor calculus by Wolfgang Hackbusch to a large extent fills the gap between theory on finite-dimensional tensor spaces and tensor computations. It also gives a comprehensive overview of numerical tensor computations. … the book is most useful as a (very rich) source book for researchers in the area. It might also be used as a textbook for a Ph.D. course … .” (Lars Eldén, Mathematical Reviews, October, 2015)
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