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* *<span style="color: red">Partition may not perfect such that every sub-matrix is a square matrix. Yet, that's not a problem, except load unbalance on each process!</span>*
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* Unbalanced Partition
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* | Unblanced Partition |
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|---------------------|
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| Data Partition <img src="https://tex.s2cms.ru/svg/%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%20c_%7B11%7D%20%26%20%7C%20%26%20c_%7B12%7D%20%5C%5C%20%0A%20%20%20%20%20%20-%20%26%20%7C%20%26%20-%20%5C%5C%0A%20c_%7B21%7D%20%26%20%7C%20%26%20c_%7B22%7D%20%5C%5C%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%20%0A%3D%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%20a_%7B11%7D%20%26%20a_%7B12%7D%20%26%20%7C%20%26a_%7B13%7D%20%26%20a_%7B14%7D%20%26%20a_%7B15%7D%20%5C%5C%20%0A%20-%20%26%20-%20%26%20%7C%20%26%20-%20%26%20-%20%26%20-%20%5C%5C%20%0A%20a_%7B21%7D%20%26%20a_%7B22%7D%20%26%20%7C%20%26a_%7B21%7D%20%26%20a_%7B24%7D%20%26%20a_%7B25%7D%20%5C%5C%20%20%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%20b_%7B11%7D%20%26%20%7C%20%26%20b_%7B12%7D%20%5C%5C%20%0A%20b_%7B21%7D%20%26%20%7C%20%26%20b_%7B22%7D%20%5C%5C%0A%20-%20%26%20%7C%20%26%20-%20%5C%5C%20%0A%20b_%7B31%7D%20%26%20%7C%20%26%20b_%7B32%7D%20%5C%5C%0A%20b_%7B41%7D%20%26%20%7C%20%26%20b_%7B42%7D%20%5C%5C%0A%20b_%7B51%7D%20%26%20%7C%20%26%20b_%7B52%7D%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)"> |
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| Data Partition <img src="https://tex.s2cms.ru/svg/c_%7B11%7D%20%3D%20%0A%5Cleft%20%5B%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%C2%A0a_%7B11%7D%20%26%20a_%7B12%7D%20%5C%5C%20%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%C2%A0%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%C2%A0b_%7B11%7D%20%5C%5C%20%0A%C2%A0b_%7B21%7D%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%5Cright%20%5D%0A%C2%A0%0A%2B%0A%C2%A0%0A%5Cleft%20%5B%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%C2%A0a_%7B13%7D%20%26%20a_%7B14%7D%20%26%20a_%7B15%7D%20%5C%5C%20%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%C2%A0%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%C2%A0b_%7B31%7D%20%5C%5C%20%0A%C2%A0b_%7B41%7D%20%5C%5C%0A%C2%A0b_%7B51%7D%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%5Cright%5D"> |
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| Process Mesh <img src="https://tex.s2cms.ru/svg/%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%20P_%7B11%7D%20%26%20P_%7B12%7D%20%5C%5C%20%0A%20P_%7B21%7D%20%26%20P_%7B22%7D%20%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)"> |
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* | Item | Object |
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|---------------------|--------------------|
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| Data Partition | <img src="https://tex.s2cms.ru/svg/%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%20c_%7B11%7D%20%26%20%7C%20%26%20c_%7B12%7D%20%5C%5C%20%0A%20%20%20%20%20%20-%20%26%20%7C%20%26%20-%20%5C%5C%0A%20c_%7B21%7D%20%26%20%7C%20%26%20c_%7B22%7D%20%5C%5C%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%20%0A%3D%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%20a_%7B11%7D%20%26%20a_%7B12%7D%20%26%20%7C%20%26a_%7B13%7D%20%26%20a_%7B14%7D%20%26%20a_%7B15%7D%20%5C%5C%20%0A%20-%20%26%20-%20%26%20%7C%20%26%20-%20%26%20-%20%26%20-%20%5C%5C%20%0A%20a_%7B21%7D%20%26%20a_%7B22%7D%20%26%20%7C%20%26a_%7B21%7D%20%26%20a_%7B24%7D%20%26%20a_%7B25%7D%20%5C%5C%20%20%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%20b_%7B11%7D%20%26%20%7C%20%26%20b_%7B12%7D%20%5C%5C%20%0A%20b_%7B21%7D%20%26%20%7C%20%26%20b_%7B22%7D%20%5C%5C%0A%20-%20%26%20%7C%20%26%20-%20%5C%5C%20%0A%20b_%7B31%7D%20%26%20%7C%20%26%20b_%7B32%7D%20%5C%5C%0A%20b_%7B41%7D%20%26%20%7C%20%26%20b_%7B42%7D%20%5C%5C%0A%20b_%7B51%7D%20%26%20%7C%20%26%20b_%7B52%7D%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)"> |
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| Data Partition | <img src="https://tex.s2cms.ru/svg/c_%7B11%7D%20%3D%20%0A%5Cleft%20%5B%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%C2%A0a_%7B11%7D%20%26%20a_%7B12%7D%20%5C%5C%20%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%C2%A0%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%C2%A0b_%7B11%7D%20%5C%5C%20%0A%C2%A0b_%7B21%7D%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%5Cright%20%5D%0A%C2%A0%0A%2B%0A%C2%A0%0A%5Cleft%20%5B%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%C2%A0a_%7B13%7D%20%26%20a_%7B14%7D%20%26%20a_%7B15%7D%20%5C%5C%20%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%C2%A0%0A%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%C2%A0b_%7B31%7D%20%5C%5C%20%0A%C2%A0b_%7B41%7D%20%5C%5C%0A%C2%A0b_%7B51%7D%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)%0A%5Cright%5D"> |
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| Process Mesh | <img src="https://tex.s2cms.ru/svg/%5Cleft%20(%0A%5Cbegin%7Bmatrix%7D%0A%20P_%7B11%7D%20%26%20P_%7B12%7D%20%5C%5C%20%0A%20P_%7B21%7D%20%26%20P_%7B22%7D%20%0A%5Cend%7Bmatrix%7D%0A%5Cright%20)"> |
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