September 2014
Intermediate to advanced
628 pages
24h 57m
English
Content preview from Numerical Linear Algebra with Applications
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19.6 The Divide-And-Conquer Method
This presentation is a summary of the divide-and-conquer method. For more in-depth coverage of this algorithm, see Refs. [1, pp. 216-228], [19, pp. 359-363], and [26, pp. 229-232].
The recursive algorithm divides a symmetric tridiagonal matrix into submatrices and then applies the same algorithm to the submatrices. We will illustrate the method of splitting the problem into smaller submatrix problems using a 5 ×5 matrix
Write A as a sum of two matrices as follows:
If we let
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