# Toeplitzmult 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Aug 30, 2007

Downloads : 4

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## This directory contains MATLAB functions for the fast ...

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 by Brian Borchers(a, b, x)

If you have a single matrix that will be multiplied times many vectors, then use

>> F=Toeplitzmult 1.0aux(a, b);

>> y1=Toeplitzmult [toeplitzmult1.0.exe]2(F, x1);

>> y2=Toeplitzmult - 0MB2(F, x2);

>> y3=Toeplitzmult 1.02(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.

The simplest case involves the multiplication of a Toeplitz matrix times a single vector. To multiply toeplitz(a, b) times x, use

>> y=Toeplitzmult by Brian Borchers(a, b, x)

If you have a single matrix that will be multiplied times many vectors, then use

>> F=Toeplitzmult 1.0aux(a, b);

>> y1=Toeplitzmult [toeplitzmult1.0.exe]2(F, x1);

>> y2=Toeplitzmult - 0MB2(F, x2);

>> y3=Toeplitzmult 1.02(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.

**• MATLAB Release: R14SP2**

**Demands:****Toeplitzmult 1.0 scripting tags:**toeplitzmult mathematics, matlab mathematics, matlab toeplitzmult, matrix, vectors, multiplication.

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