[[File:Matrix multiplication on a cross-wire two-dimensional array.png|thumb|240px|Matrix multiplication completed in 2n-1 steps for two n×n matrices on a cross-wired mesh.]]
There are a variety of algorithms for multiplication on [[Mesh networking|meshes]]. For multiplication of two ''n''×''n'' on a standard two-dimensional mesh using the 2D [[Cannon's algorithm]], one can complete the multiplication in 3''n''-2 steps although this is reduced to half this number for repeated computations.<ref>{{cite journal | last1 = Bae, | first1 = S.E., | last2 = Shinn | first2 = T.-W. Shinn,| last3 = Takaoka | first3 = T. Takaoka| year = (2014)[| title = A faster parallel algorithm for matrix multiplication on a mesh array | url = https://www.sciencedirect.com/science/article/pii/S1877050914003858/pdf?md5=4d641ad288db14733fb2f82ee445c258&pid=1-s2.0-S1877050914003858-main.pdf&_valck=1 A| fasterjournal parallel= algorithmProcedia forComputer matrixScience multiplication| onvolume a= mesh29 array].| Procediaissue Computer= Science| 29:pages 2230-2240= 2230–2240 }}</ref> The standard array is inefficient because the data from the two matrices does not arrive simultaneously and it must be padded with zeroes.
The result is even faster on a two-layered cross-wired mesh, where only 2''n''-1 steps are needed.<ref>{{cite journal | last1 = Kak, | first1 = S.(| year = 1988)[| title = A two-layered mesh array for matrix multiplication | url = http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.88.8527&rep=rep1&type=pdf A| two-layeredjournal mesh= arrayParallel forComputing matrix| multiplication].volume Parallel Computing= 6:383-385| issue = | pages = 383–385 }}</ref> The performance improves further for repeated computations leading to 100% efficiency.<ref>Kak, S. (2014) Efficiency of matrix multiplication on the cross-wired mesh array. https://arxiv.org/abs/1411.3273</ref> The cross-wired mesh array may be seen as a special case of a non-planar (i.e. multilayered) processing structure.<ref>{{cite journal | last1 = Kak, | first1 = S.(| year = 1988)[| title = Multilayered array computing | url = http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.4753&rep=rep1&type=pdf Multilayered| arrayjournal computing].= Information Sciences | volume = 45:347-365| issue = | pages = 347–365 }}</ref>
