Abstract
Any function can be approached by finite element to any accuracy, because space of finite element of rough division is included in the space of fine division, one can get multi-solution theory by finite element method. The multi-solution theory bases on the usually finite element theory will result in a lot oft calculation. Representation theory of group is used to translate the bases of finite element to orthogonal bases and by this method a multi-solution theory is developed bases on finite element method. The theory can be applied to two-dimension signal compact.
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