It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth, i.e., the approximate solution may lack many details that the desired exact solution might possess. Two different approaches, both referred to as fractional Tikhonov methods have been introduced to remedy this shortcoming. This paper investigates the convergence properties of ...

A novel method of the IIR filter design using the genetic algorithm is described in the paper. Newly, a simplex direct search method is included to the algorithm to enable its faster convergence. The design procedure is implemented in the MATLAB program environment. The genetic algorithm applied is able to find a solution of the task successfully. Filter coefficients quantization process is inc...

In this paper, we treat a design problem for IIR digital filters described by rational transfer function in discrete space. First, we form the filter design problem using the modified least-squares (MLS) criterion and express it as the quadratic form with respect to the numerator and denominator coefficients. Next, we show the relaxation method using the Lagrange multiplier method in order to s...

We propose in this paper an effective meshless and integration-free method for the numerical solution of multidimensional inverse heat conduction problems. Due to the use of fundamental solutions as basis functions, the method leads to a global approximation scheme in both the spatial and time domains. To tackle the ill-conditioning problem of the resultant linear system of equations, we apply ...

This work is concerned with nonlinear inverse problems where the solution is assumed to have a sparse expansion with respect to several preassigned bases or frames. We develop a scheme which allows to minimize a Tikhonov functional where the usual quadratic regularization term is replaced by one–homogeneous (typically weighted `p, 1 ≤ p ≤ 2) penalties on the coefficients (or isometrically trans...

We consider a new idea for solving Tikhonov regularized discretized ill-posed problems. The optimization problem is formulated as a nonlinear least squares problems containing the Tikhonov regularization parameter λ. In order to find the size of the regularization parameter and attain good convergence in the optimization method we use the nonlinear Land a-curve. The nonlinear L-curve is a direc...