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One can show that in a general sparse matrix, it is straightforward to preserver the "end" zeros
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000...000X000...000XXX000...000X000...000 shows structure of a row of A in 2D Laplace example
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The first and last zeros can be explicitly taken into account by setting range of for loops properly
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The inside zeros "fill" i.e. become nonzero during process of Gaussian elimination
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Thus if bandwidth B i.e.
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000...000X000...000XXX000...000X000...000
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Then computational complexity is not N3 as for a full (no zeros accounted) but NB2
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