  This paper begins by reviewing numerous theoretical advancements in the field
of multivariate splines, primarily contributed by Professor Larry L. Schumaker.
These foundational results have paved the way for a wide range of applications
and computational techniques. The paper then proceeds to highlight various
practical applications of multivariate splines. These include scattered data
fitting and interpolation, the construction of smooth curves and surfaces, and
the numerical solutions of various partial differential equations, encompassing
both linear and nonlinear PDEs. Beyond these conventional and well-established
uses, the paper introduces a novel application of multivariate splines in
function value denoising. This innovative approach facilitates the creation of
LKB splines, which are instrumental in approximating high-dimensional functions
and effectively circumventing the curse of dimensionality.
