Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology / edited by Martina Lanini, Carla Manni, Henry Schenck.

Format:

Book

Author/Creator:

Lanini, Martina.

Contributor:

Manni, Carla.

Schenck, Henry.

Series:

Springer INdAM Series, 2281-5198 ; 60

Language:

English

Subjects (All):

Approximation theory.

Numerical analysis.

Algebra.

Geometry.

Topology.

Approximations and Expansions.

Numerical Analysis.

Local Subjects:

Approximations and Expansions.

Numerical Analysis.

Algebra.

Geometry.

Topology.

Physical Description:

1 online resource (333 pages)

Edition:

1st ed. 2024.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2024.

Summary:

The book, based on the INdAM Workshop "Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology" provides a bridge between different communities of mathematicians who utilize splines in their work. Splines are mathematical objects which allow researchers in geometric modeling and approximation theory to tackle a wide variety of questions. Splines are interesting for both applied mathematicians, and also for those working in purely theoretical mathematical settings. This book contains contributions by researchers from different mathematical communities: on the applied side, those working in numerical analysis and approximation theory, and on the theoretical side, those working in GKM theory, equivariant cohomology and homological algebra.

Contents:

Introduction

Bernstein Bézier form and its role in studying multivariate splines

The algebra of splines group actions and homology

A study on approximation by quartic splines defined on refined triangulations

Construction of 2D explicit cubic

Overlap Splines and Meshless Finite Difference

A characterization of linear independence of THB splines in R n

Restriction and Extension for planar splines on triangulations

Supersmoothness of multivariate splines

Using Geometric Symmetries to Achieve Super Smoothness for Cubic Powell-Sabin Splines

Finite element diagram chasing

On tensor product bases of PHT splinespaces

Momentum graphs, Chinese remainder theorem and the surjectivity of the restriction map

A Parsimonious Approach to $C^2$ Cubic Splines on Arbitrary Triangulations

Alcove Walks and GKM Theory for Affine Flags

Open problems in splines.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Lanini, Martina Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology

ISBN:

9789819765089

OCLC:

1485004568