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We introduce the combination technique for the numerical solution of d-dimensional eigenproblems on sparse grids.
The core of the algorithms relies on adaptive refinement of sparse grids.
Sparse grids are known to require only few unknowns in order to obtain good approximation qualities.
To circumvent the curse of dimensionality of full tensor product grids, we use the concept of sparse grids.
As a result, a much easier data structure the array can be used to store the sparse grids.
Ian Ashdown has obtained good results in luminaire research by using BRDFs and luminaire photometry data sampled on rather sparse grids [Ashdown 92].
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By introducing a new concept of layer to sparse grid points, the sparse grid construction can become much efficient.
A sparse grid causes interpolation problems and dense grids increase the calibration effort.
The introduction of separable functions also solves the issue of the non-rectangular sparse grid.
They are designed to exploit low effective dimensions and include sparse grid methods as special case.
Moreover, both of the sparse grid construction and interpolation algorithms can be done in parallel.
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