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# Toeplitzmult 1.0

Date Added: April 21, 2013  |  Visits: 175

This directory contains MATLAB functions for the fast multiplication of a Toeplitz matrix times a vector. By using these routines you can avoid storing the entire matrix (using two vectors of lenght n rather than a matrix of size n*n), and also dramatically speedup the multiplication. The algorithm used here runs in O(n*log(n)) time instead of the O(n^2) time required by conventional matrix multiplication.The simplest case involves the multiplication of a Toeplitz matrix times a single vector. To multiply toeplitz(a,b) times x, use>> y=toeplitzmult(a,b,x)If you have a single matrix that will be multiplied times many vectors, then use>> F=toeplitzmultaux(a,b);>> y1=toeplitzmult2(F,x1);>> y2=toeplitzmult2(F,x2);>> y3=toeplitzmult2(F,x3);... The script example.m demonstrates the use of these functions.Note that this code works correctly with matrices and vectors that are real or complex. However, due to round-off errors, the product might have a small imaginary component even though a,b, and x are all real. To correct this, simply use real(toeplitz(a,b,x))A good introduction to how these algorithms work can be found in the book "Matrix Computations, 3rd ed." by Golub and Van Loan.

 Requirements: No special requirements Platforms: Matlab Keyword: Complex,  Correctly,  Demonstrates,  Dtoeplitzmult,  Dtoeplitzmultauxab,  Errors,  Matrices,  Roundoff,  Works Users rating: 0/10