Numerical Approximation to Multivariate Functions Using Fluctuationlessness Theorem with a Trigonometric Basis Function to Deal with Highly Oscillatory Functions - (:unkn) unknown (WORLD SCIENTIFIC AND ENGINEERING ACAD AND SOC, 2009)
Recently developed Fluctuation Free Matrix Representation Method can be used in approximating the integrals appearing in the multiple remainder terms of the Multivariate Taylor Expansion. This provides us with a new numerical approximation method for multivariate functions. In this work a trigonometric basis set, rather than a polynomial one is chosen in order to deal with highly oscillatory functions.
Keywords: Multivariate Functions; Fluctuationlessness Theorem; Numerical Approximation; Explicit Remainder Term; Taylor Expansion; Trigonometric Basis Set; INTEGRATION