On Orthogonal Polynomials and Finite Moment Problem

Background: This paper is an improvement of a previous work on the problem recovering function or probability density from finite number its geometric moments, [1]. The worked solved with help B-Spline theory which great approach as long resulting linear system not very large. In this work, two solution algorithms based approximate representation target distribution via orthogonal expansion are provided. One primary application reconstruction Particle Size Distribution (PSD), occurring in chemical engineering applications. Another Radon transform image at unknown angle using moments known angles leads to form limited data. Objective: aim recover moments. Methods: tool approach. Shifted-Legendre Polynomials and Chebyshev bases for used study. Results: A high degree accuracy has been obtained without facing possible ill-conditioned system, case many typical approaches solving problem. fact, normalized template f interval [0, 1], reconstructed ; measured domains. moment domain, error (difference between ) zero. other measure standard difference norm -space || - can be ≈ 10 -6 less. Conclusion: discusses PSD application. Linear transformations were used, needed, so that supported unit α] some choice α. transformation forces sequence vanish. Then, Scaled Shifted Legendre Polynomials, well developed. result shows good different types synthetic functions. It believed up fifteen safe reliable.