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Unformatted text preview: A = x x . . . x x x . . . x x x 0 0 . . . 0 0 . . . x x Consider elimination applied to a column of the matrix. There is only one row below that column and this row has at most two nonzero elements. Thus, elimination takes constant time for this column. The total cost of elimination is proportional to n because there are n columns. Back-substitution also has cost proportional to n because the rows have at most two non-zero elements. Hence, the total cost to solve a system where the coeﬃcient matrix is tridiagonal is proportional to n . 2...
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This note was uploaded on 01/31/2012 for the course COMS 3251 taught by Professor Anargyrospapageorgiou during the Fall '11 term at Columbia.
- Fall '11