Chapter 62
Fast Algorithms for Structured Matrix Computations
Michael Stewart
Georgia State University
A structured matrix is an m×n matrix with elements that can be determined from substantially fewer than mn parameters. This is a broad definition that includes sparse matrices, matrices with displacement structure, matrices with rank structure, and numerous types of matrices with specialized structure. Many common matrix operations can be performed using fast algorithms that exploit matrix structure to achieve asymptotic speed-up relative to conventional algorithms. For matrices with either displacement structure or rank structure, there are fast algorithms for the solution of linear systems, inversion, QR factorization, and matrix-vector multiplication. ...
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