2015/03/27 by Ildar R. Muftahov, Ildar Muftahov, Denis Sidorov +6
Computer Science · Engineering · Mathematics · #47A52 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Thermoelastic and Magnetoelastic Phenomena #math.FA #msc:47A52
paper · pdf · doi:10.48550/arxiv.1503.07938
openalex publication_date 2015/03/27 · arxiv created 2015/04/13 · arxiv updated 2015/04/14 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
One of the most common problems of scientific applications is computation of the derivative of a function specified by possibly noisy or imprecise experimental data. Application of conventional techniques for numerically calculating derivatives will amplify the noise making the result useless. We address this typical ill-posed problem by application of perturbation method to linear first kind equations Ax=f with bounded operator A. We assume that we know the operator A and source function f only such as ||A - A||≤ δ1, ||f-f||< δ2. The regularizing equation Ax + B(α)x = f possesses the unique solution. Here α∈ S, S is assumed to be an open space in ℝn, 0 ∈ S, α= α(δ). As result of proposed theory, we suggest a novel algorithm providing accurate results even in the presence of a large amount of noise.