New Approach To A Class Of Matrices

The displacement structure is extended to a Kronecker matrix W ⊗ Z. A new class of Kronecker-like matrices with the displacement rank r, r < n will be formulated and presented. The computational complexity of multiplication with vectors for Kronecker-like matrices has been accelerated. Applying the displacement, which was originally discovered by Kailath, Kung and Morf [15], a new superfast algorithm for the multiplication of a Kronecker-like matrix of the size n1×n1 over a field with a vector will be designed. The memory space cost of the number of the elements stored for a Kronecker-like matrix of the size n1×n1 over a field is O(rn). The cost of the number of the arithmetic operations for the product of a Kronecker-like matrix with the displacement rank r and a vector is reduced dramatically to O(rn).

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