“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)
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.
About the Author
The author is working in the field of numerical mathematics for partial differential equations and integral equations. He has published monographs, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and about the technique of hierarchical matrices.
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