Mehdi Hamzehnejad - Department of Mathematic, Graduate University of Advanced Technology, Kerman, Iran.
Mohammad Mehdi Hosseini - Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.
Abbas Salemi - Department of Applied Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.

We estimate a function f with N independent observations by using Leg-endre wavelets operational matrices. The function f is approximated with the solution of a special minimization problem. We introduce an explicit expression for the penalty term by Legendre wavelets operational matrices. Also, we obtain a new upper bound on the approximation error of a differentiable function f using the partial sums of the Legendre wavelets. The validity and ability of these operational matrices are shown by several examples of real-world problems with some constraints. An accurate ap-proximation of the regression function is obtained by the Legendre wavelets estimator. Furthermore, the proposed estimation is compared with a non-parametric regression algorithm and the capability of this estimation is illustrated.

Legendre wavelet, Operational matrix, Wavelet approximation, Regression function, error analysis