# High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs

## Related Articles

- Interpolation and partial differential equations. Maligranda, Lech; Persson, Lars Erik; Wyller, John // Journal of Mathematical Physics;Sep94, Vol. 35 Issue 9, p5035
One of the main motivations for developing the theory of interpolation was to apply it to the theory of partial differential equations (PDEs). Nowadays interpolation theory has been developed in an almost unbelievable way {see the bibliography of Maligranda [Interpolation of Operators and...

- On Polynomial Projectors That Preserve Homogeneous Partial Differential Equations. Dinh Dung; Calvi, Jean-Paul; Nguyên Tiên Trung // Vietnam Journal of Mathematics;Mar2004, Vol. 32 Issue 1, p109
Gives a characterization of Abel-Gontcharoff projectors as the only Birkhoff polynomial projectors that preserve all homogeneous partial differential equations. Space of interpolation conditions; Concept of pairing of Banach spaces; Discrete functional.

- A class of index transforms with Whittaker's function as the kernel. Srivastava, HM; Vasil'ev, YV; Yakubovich, SB // Quarterly Journal of Mathematics;Sep98, Vol. 49 Issue 195, p375
Focuses on the transformation of a class of index using the Whittaker function as the kernel. Assumption of function f to be in Lebesgue space; Convergence of integrals; Transformation of the index in Hilbert spaces; Establishment of the Plancherel theorem analog in Fourier integrals.

- SURFACE INTERPOLATION USING PARTIAL DIFFERENTIAL EQUATION WITH POSITIVITY PRESERVING CUBIC BÃ‰ZIER CURVES BOUNDARY CONDITION. Saaban, Azizan; Noraziah Haji Man; Abdul Karim, Samsul Ariffin // Far East Journal of Mathematical Sciences;Apr2013, Vol. 75 Issue 2, p257
This paper proposes the sufficient conditions for positivity preserving cubic boundary curves defined on rectangular grid using a polynomial solution of fourth order linear PDEs in order to improve the positivity preserving of the interpolating surface. We derive a sufficient condition on...

- The numerical stability of barycentric Lagrange interpolation. Higham, Nicholas J. // IMA Journal of Numerical Analysis;Oct2004, Vol. 24 Issue 4, p547
The Lagrange representation of the interpolating polynomial can be rewritten in two more computationally attractive forms: a modified Lagrange form and a barycentric form. We give an error analysis of the evaluation of the interpolating polynomial using these two forms. The modified Lagrange...

- Exact Lebesgue constants for interpolatory â„’-splines of third order. Kim, V. A. // Mathematical Notes;Jul2008, Vol. 84 Issue 1-2, p55
In this paper, we obtain the Lebesgue constants for interpolatory â„’-splines of third order with uniform nodes, i.e., the norms of interpolation operators from C to C describing the process of interpolation of continuous bounded and continuous periodic functions by â„’-splines of...

- On the Order of the Lebesgue Constants for Interpolation by Algebraic Polynomials from Values at Uniform Nodes of a Simplex. Baidakova, N. V. // Mathematical Notes;May/Jun2005, Vol. 77 Issue 5/6, p751
For interpolation processes by algebraic polynomials of degree n from values at uniform nodes of an m-simplex, where m â‰¥ 2, we obtain the order of growth in n of the Lebesgue constants, which coincides with that in the one-dimensional case for which Turetskii obtained an asymptotics earlier.

- Lower bound for the Lebesgue function of an interpolation process with algebraic polynomials on equidistant nodes of a simplex. Baidakova, N. // Mathematical Notes;Jul2012, Vol. 92 Issue 1/2, p16
For an interpolation process with algebraic polynomials of degree n on equidistant nodes of an m-simplex for m â‰¥ 2, we obtain a pointwise lower bound for the Lebesgue function similar to the well-known estimate for interpolation on a closed interval.

- A Taste of Ideal Projectors. // Journal of Concrete & Applicable Mathematics;Jan2011 Supplement, p125
No abstract available.