Name of the matrix:

Matrix with algebraic decay

Pattern:

 

$$a_{ij} = a_{i-j} = \frac{2\pi}{\sigma[4\sigma^2+(i-j)^2]}, \qquad i,j=0,1,\ldots$$

Properties:

symmetric, positive definite, the asymptotic condition number is

$${\mathrm{cond}}(A) = \cosh(2\pi\sigma)$$

Source/utilization:

test for the solution of linear systems

References:

 
C.V.M. van der Mee, Z.M. Nashed and S. Seatzu, Sampling expansions in unitarily translation invariant reproducing kernel Hilbert spaces, Adv. Comput. Math. 19(4), 355-372 (2003).
C.V.M. van der Mee and S. Seatzu, A method for generating infinite positive self-adjoint test matrices and Riesz bases, SIAM J. Matr. Anal. Appl., to appear.

Matlab:

t=tptest(3,n,sigma)