Liu, X. (2001) Bivariate Cardinal Spline Functions for Digital Signal Processing. In: Kopotum, K., Lyche, T. and Neamtu, M., Eds., Trends in Approximation Theory, Vanderbilt University, Nashville, 261-271.

has been cited by the following article:

• TITLE: Solving Systems of Volterra Integral Equations with Cardinal Splines

  AUTHORS: Xiaoyan Liu, Zhi Liu, Jin Xie

  KEYWORDS: Spline Functions, Integral Equations, Numerical Methods

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.11, November 23, 2015

  ABSTRACT: This work is a continuation of the earlier article [1]. We establish new numerical methods for solving systems of Volterra integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is acquired for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are applied in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. We demonstrated the value of the methods using several examples.