| 1 |
Consider Ax = b solved "directly" which is Gaussian elimination where one succesively removes
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x1 from Equation 2 to N,
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x2 from Equations 3 to N etc.
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| 2 |
Then this has memory requirement of order N2 and computational complexity of order N3
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| 3 |
This is modified somewhat when you consider matrices A with a lot of zeroes and try hard to exploit these zeros i.e. avoid doing calculations which are irrelevant as adding or multiplying by zero
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| 4 |
Of course this cannot be done by testing on matrix element being zero as modern computers do floating point arithmetic faster than or at least as fast as test!
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| 5 |
Rather one arranges loops to not include zero elements -- if possible!
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