Matrix is commonly used in scientific computing and engineering calculation. We are not concerned about data itself in data-structures, but how to store the elements in it, and make all the operations run effectively. The main task of the compressed storage is make more of the same nonzero-elements share the same storage unit according the distribution of elements, at the same time lots of zero-elements don't allocate storage space. In this article, we discussed the multidimensional compressed

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... torage of upper-half banded matrix, and obtained the row-major compressed storage address mapping functions and columnmajor compressed storage address mapping functions for the first time. Also, the two kinds of compressed storages have high compression storage ratio. We hope the conclusion can provide the basic data storage theory for engineering calculation and scientific computing.