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Matrix is a mathematical object, commonly used in scientific computing and engineering calculation. In the data structure we are not interested in data itself, but how to store the elements in the matrix, and make the various operations can run effectively. The main purpose of the compressed storage is to make more of the same nonzero elements share the same storage unit according to the distribution of matrix element, while the zero elements don't allocate storage space. In this paper, we studied the multi-vector compressed storage problems of lower half banded matrix, and obtained the row and column priority compressed storage address mapping function for the first time. The compressed storage structures have high compression ratio. The conclusions hope to provide the basic theory of data compression storage for the computer research workers. 1.DEFINITION OF HALF BANDED MATRIX Matrix is a mathematical object, commonly used in scientific computing and engineering calculation. We are not interested in data type or value in the data structure, but how to store the elements in the matrix. When programming in a high-level language, often use a two-dimensional array to store the elements in the matrix. If adopt this method of storage, we can random access each data element, thus can easily realize operations of the matrix. But, when there are a large number of zero elements in the matrix and have regular distribution, if still use a two-dimensional array to store the matrix, a particular element will consume large amounts of storage unit. For high order matrix, the storage method is not only waste storage unit, but also takes a lot of time for invalid computation, it is obviously not desirable. In order to save the storage space, we need to compress storage for such matrix. The main purpose of the compressed storage is to make more of the same nonzero elements share the same storage unit according to the distribution of matrix element, while the zero elements don't allocate storage space. In this paper, we studied the compressed storage problems of lower banded matrix, and obtained the corresponding storage address mapping functions. The lower half banded matrix is evolved from the banded matrix. The elements come from the banded matrix diagonal line and lower part only. The elements along the diagonal direction of the matrix regular distribution in the one side of the diagonal. In a matrix A of order n, if there exists a maximum positive number m, ai,j is a matrix element, when it meets 0≤i-j≤m-1, ai,j is an ordinary integer, the rest elements are 0 or a constant integer. The A is called lower half banded matrix. The integer m is called bandwidth. If the order is n, the bandwidth is m, the data elements in the half band matrix A compressed storage into a multi-vector B. By the simple calculation, the size of storage space for B vector is (m×n). 36

The Multi-vector Compressed Storage of Lower Half Banded Matrix