ORTHOGONAL ZERO INTERPOLANTS AND APPLICATIONS

Subject Areas : International Journal of Mathematical Modelling & Computations

M. A. Bokhari ¹ , H. Al-Attas ²

1 - KFUPM, Dhahran Saudi Arabia Deptartment of Mathematics & Statatistic
2 - KFUPM, Dhahran Saudi Arabia Deptartment of Mathematics & Statatistic

Received: 2016-04-12 Accepted : 2016-04-12 Published : 2011-12-22

Keywords: Ortogonal zero interpolant, 3-term recurrence relation, constrained least squares approximation, Parseval equality, Jacobi matrix, Gauss-Radau/Lobatto rules,

Abstract :

Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical and computational aspects of OZI’s and also discuss their structure and significance at the multiple nodes.