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The performance of GiMMiK's kernels is particularly apparent in a block-by-panel type of matrix multiplication, where the block matrix is typically small (e.g. dimensions of 96×64).
Because the algorithm is based on simple matrix-vector multiplication, where the matrix is | E | × | E | in size, the computation of the Green's function for small trees such as the binary trees used here to within ε = 10 − 15 only takes a fraction of a second.
In the special case where n1 = n3 = 1, the matrix multiplication X ⊗ Y is also called a vector multiplication (where the resulting matrix Z contains a single element).
Keeping the areas constant after multiplication is done by multiplying the new area of each age class with ∑ Area ∑ Area after multiplication where the sums are build for each region.
Big squared/graph paper allows the kids to start a project about multiplication where the "8" sequences can be drawn and decorated to make the teaching points intuitively clear.
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The evaluation of the objective function in Eqs. 12 and 13 needs two multiplications where the factor 1/ 3N) is pre-computed.
The new (lambda) chromosomes are as follows in the chromosome pool after multiplication (where (lambda) is the number of the new individual chromosomes): A_{3}^{(t)} = left{ {left.
The function of this systolic array is to perform the triple matrix multiplication, where matrix S has the band-Toeplitz structure [5, 6] with the width of the non-zero strip over the azimuth frame equal to Following the methodology addressed in the previous section, the triple matrix multiplication corresponding to the MSF function can be implemented using a cascade systolic array.
Further speed gains are made by optimising the calculation of the normal matrix (A A t ), a special case of a general matrix multiplication where only half of the values need to be computed.
Data transports from the result register to the general-purpose register are completely scraped for both additions (dead result move elimination), as the results are used just once in multiplication, where they are transported directly from the result register of the adder.
Using the Coppersmith-Winograd algorithm [ 12] for matrix multiplication, where ω = 2.376, this yields a running time of O(n2.688).
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