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Setia, A., Liu, Y.-C. and Vatsala, A.S. (2014) Numerical Solution of Fractional Integro-Differential Equations with Nonlocal Boundary Conditions. Journal of Fractional Calculus and Applications, 5, 155-165.

has been cited by the following article:

• TITLE: Continuous-Time and Discrete-Time Singular Value Decomposition of an Impulse Response Function

  AUTHORS: Rogelio Luck, Yucheng Liu

  KEYWORDS: Singular Value Decomposition, Impulse Response Function, Green’s Function, Toeplitz Matrix, Hankel Matrix

  JOURNAL NAME: Applied Mathematics, Vol.12 No.4, April 28, 2021

  ABSTRACT: This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.