Multiple root finder algorithm for Legendre and Chebyshev polynomials via Newton's method.
Multiple Zeros and Applications to Optimal Linear Functionals.
Multiple-Precision Correctly rounded Newton-Cotes quadrature
Numerical integration is an important operation for scientific computations. Although the different quadrature methods have been well studied from a mathematical point of view, the analysis of the actual error when performing the quadrature on a computer is often neglected. This step is however required for certified arithmetics. We study the Newton-Cotes quadrature scheme in the context of multiple-precision arithmetic and give enough details on the algorithms and the error bounds to enable software...
Multivariate approximation theory with -splines
Multivariate Birkhoff-Lagrange interpolation schemes and Cartesian sets of nodes.
Multivariate smooth interpolation that employs polyharmonic functions
We study the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomial terms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example...
Multivariate spline functions, B-spline bases and polynomial interpolations II