In contrast, since the proposed framework uses

matrix operations, especially if combining the

matrix operation features of Matlab, the time cost does not increase too much when the number of nodes becomes large.

Indeed, our homomorphic multiplication will not cause the tangly modulus problem existent in Costache and Smart's solution [22], because these two different modular operations (in terms of moduli _p) can be partitioned by our

matrix operation but cannot be by the tensor product used by them.

Furthermore, we deduce the indexing simplified ML detector of the algebraic orthogonal USTM constellation which only needs to operate several complex-values and get rid of the

matrix operation. In Section 6, we show the simulation testing results between the searching and algebraic orthogonal USTM constellations which indicate that the searching constellation is superior to the algebraic that in both chordal Frobenius distance spectrum and performance with regard to symbol error probability and signal noise ratio.

In the above

matrix operation [cross product], an element [t.sub.ik] is calculated as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Fuzzy

matrix operation for R is carried out with the fuzzy judgment matrix B of the system being obtained:

(15) and (16) without the requirement of any

matrix operation and manipulation.

Although PCA expresses several distinctive outcomes, one of the drawbacks is over a high complexity due to larger

matrix operation. A large amount of memory is also required since the memory requirement grows with the image quality, high resolution, and the number of training images used for image matching or classification [10, 11].

We solve the

matrix operation identification problem for matrix multiplication of different kinds as well as matrix addition and subtraction.

time dependent ones) then system of equations cannot be solved by the methods using the

matrix operation. As a solver for their solution the following numerical methods can serve, completed by fictitious exciting functions method making possible numerical solution of this DE system with nonstationary matrices [1], [2], [5].

we have implemented

matrix operation algorithms based on row partition experiment in order to further gain to inside .

Another well-known

matrix operation closely resembling the reorderable matrix permutation is Gaussian elimination, where rows and columns are multiplied by and subtracted from each other.

To achieve homomorphic

matrix operation, the pubic key of matrix GSW-FHE scheme includes the ciphertexts that encrypt partial information of the secret key, so the matrix GSW-FHE scheme resorts to circular security assumption, but formal circular security proof was not given, and it remains an open problem.