An Efficient Algorithm for the Regularization of Ill-Conditioned Least Squares Problems with Triangular Toeplitz Matrix

Ill-conditioned least squares problems, where the matrix is triangular and has Toeplitz structure, arise when certain Volterra integral equations with stationary kernel are discretized. Tikhonov–Phillips regularization can be used to stabilize the solution. An efficient algorithm for computing regularized solutions of such problems is described. The number of arithmetic operations required is O(n² ), where n is the dimension of the matrix. A numerical example is given, where an inverse heat conduction problem is solved.