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The product of two greenhouse matrices?

The algorithm O(n log n)for the product of the Toeplitz matrix and the vector of the correct length is well known: place it in the circulant matrix, multiply it by the vector (and subsequent zeros) and return the top nelements of the product.

I find the problem to find the best (temporary) algorithm for multiplying two Toeplitz matrices of the same size.

Can someone give me an algorithm for this?

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Here there is an O (n ^ 2) -time algorithm.

, -n (2n-1), -. O (1).

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e f g h i    o p q r s
d e f g h    m o p q r
c d e f g    l m o p q
b c d e f    k l m o p
a b c d e    j k l m o

1,1 eo + fm + gl + hk + ij. 2,2 dp + eo + fm + gl + hk, 1,1 ij dp. 3,3 cq + dp + eo + fm + gl, 2,2 hk cq. 4,4 br + cq + dp + eo + fm ..

, .

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