Given
numbers ,
where ,
..., ,
0, 1, ..., ,
a Toeplitz matrix is a matrix which has constant values
along negative-sloping diagonals, i.e., a matrix of the
form
can be solved with
operations. Typical problems modelled by Toeplitz matrices include the numerical
solution of certain differential and integral equations (regularization of inverse
problems), the computation of splines, time
series analysis, signal and image processing, Markov
chains, and queuing theory (Bini 1995).
numbers 
,
where 
,
..., 
,
0, 1, ..., 
,
a Toeplitz matrix is a matrix which has constant values
along negative-sloping diagonals, i.e., a matrix of the
form
![[a_0 a_(-1) a_(-2) ... a_(-n+1); a_1 a_0 a_(-1) ... |; a_2 a_1 a_0 ... a_(-2); | ... ... ... a_(-1); a_(n-1) ... a_2 a_1 a_0].](/images/equations/ToeplitzMatrix/NumberedEquation1.svg)
operations. Typical problems modelled by Toeplitz matrices include the numerical
solution of certain differential and integral equations (regularization of inverse
problems), the computation of splines, time
series analysis, signal and image processing, Markov
chains, and queuing theory (Bini 1995).
