Browsing Oberwolfach Reports by MSC "41"

Now showing items 1-18 of 18

    • 1638a - Adaptive Algorithms 

      [OWR-2016-44] Workshop Report 2016,44 (2016) - (18 Sep - 24 Sep 2016)
      Overwhelming empirical evidence in computational science and engineering proved that self-adaptive mesh-generation is a must-do in real-life problem computational partial differential equations. The mathematical understanding ...

    • 2207a - Interpolation, Approximation, and Algebra 

      [OWR-2022-7] Workshop Report 2022,7 (2022) - (13 Feb - 19 Feb 2022)
      This report involves two concepts of geometric modeling: multi-variate data interpolation by polynomials, and the study of generalized bary\-centric coordinates. These topics are connected to a wide range of of applications, ...

    • 1627b - Learning Theory and Approximation 

      [OWR-2016-33] Workshop Report 2016,33 (2016) - (03 Jul - 09 Jul 2016)
      The main goal of this workshop – the third one of this type at the MFO – has been to blend mathematical results from statistical learning theory and approximation theory to strengthen both disciplines and use synergistic ...

    • 1226 - Learning Theory and Approximation 

      [OWR-2012-31] Workshop Report 2012,31 (2012) - (24 Jun - 30 Jun 2012)
      Learning theory studies data structures from samples and aims at understanding unknown function relations behind them. This leads to interesting theoretical problems which can be often attacked with methods from Approximation ...

    • 0827b - Learning Theory and Approximation 

      [OWR-2008-30] Workshop Report 2008,30 (2008) - (29 Jun - 05 Jul 2008)
      Mathematical analysis of learning algorithms consists of bias measured by various kinds of approximation errors and variance investigated by probability and statistical analysis. This workshop has dealt with new developments ...

    • 1929b - Mathematical Foundations of Isogeometric Analysis 

      [OWR-2019-33] Workshop Report 2019,33 (2019) - (14 Jul - 20 Jul 2019)
      Isogeometric analysis is a recent technology for numerical simulation, unifying computer aided design and finite element analysis. It offers a true design-through-analysis pipeline by employing the same representation ...

    • 1606c - Mini-Workshop: Mathematical Foundations of Isogeometric Analysis 

      [OWR-2016-8] Workshop Report 2016,8 (2016) - (07 Feb - 13 Feb 2016)
      Isogeometric Analysis (IgA) is a new paradigm which is designed to merge two so far disjoint disciplines, namely, numerical simulations for partial differential equations (PDEs) and applied geometry. Initiated by the ...

    • 2119b - Mini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control (hybrid meeting) 

      [OWR-2021-24] Workshop Report 2021,24 (2021) - (09 May - 15 May 2021)
      Dissipation of energy --- as well as its sibling the increase of entropy --- are fundamental facts inherent to any physical system. The concept of dissipativity has been extended to a more general system theoretic setting ...

    • 1507a - Mini-Workshop: Modern Applications of s-numbers and Operator Ideals 

      [OWR-2015-6] Workshop Report 2015,6 (2015) - (08 Feb - 14 Feb 2015)
      The main aim of this mini-workshop was to present and discuss some modern applications of the functional-analytic concepts of $s$-numbers and operator ideals in areas like Numerical Analysis, Theory of Function Spaces, ...

    • 2339b - Mini-Workshop: Multivariate Orthogonal Polynomials: New synergies with Numerical Analysis 

      [OWR-2023-43] Workshop Report 2023,43 (2023) - (24 Sep - 29 Sep 2023)
      Multivariate polynomials and, in particular, multivariate orthogonal polynomials (MOPs) are research areas within the fields of special functions, Lie groups, quantum groups, computer algebra to name only some of them. ...

    • 2342c - Mini-Workshop: Nonlinear Approximation of High-dimensional Functions in Scientific Computing 

      [OWR-2023-48] Workshop Report 2023,48 (2023) - (15 Oct - 20 Oct 2023)
      Approximation techniques for high dimensional PDEs are crucial for contemporary scientific computing tasks and gained momentum in recent years due to the renewed interest in neural networks. It seems that especially ...

    • 1713 - Multiscale and High-Dimensional Problems 

      [OWR-2017-17] Workshop Report 2017,17 (2017) - (26 Mar - 01 Apr 2017)
      High-dimensional problems appear naturally in various scientific areas. Two primary examples are PDEs describing complex processes in computational chemistry and physics, and stochastic/ parameter-dependent PDEs arising ...

    • 1517a - Multivariate Splines and Algebraic Geometry 

      [OWR-2015-21] Workshop Report 2015,21 (2015) - (19 Apr - 25 Apr 2015)
      Multivariate splines are effective tools in numerical analysis and approximation theory. Despite an extensive literature on the subject, there remain open questions in finding their dimension, constructing local bases, and ...

    • 1503 - New Discretization Methods for the Numerical Approximation of PDEs 

      [OWR-2015-2] Workshop Report 2015,2 (2015) - (11 Jan - 17 Jan 2015)
      The construction and mathematical analysis of numerical methods for PDEs is a fundamental area of modern applied mathematics. Among the various techniques that have been proposed in the past, some – in particular, finite ...

    • 0645 - Qualitative Assumptions and Regularization in High-Dimensional Statistics 

      [OWR-2006-49] Workshop Report 2006,49 (2006) - (05 Nov - 11 Nov 2006)
      Important and exciting developments are currently underway in nonparametric statistics involving inter-play between qualitative constraints, penalization, and regularization methods. Some of these developments are taking ...

    • 1538 - Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws 

      [OWR-2015-41] Workshop Report 2015,41 (2015) - (13 Sep - 19 Sep 2015)
      The development of reliable numerical methods for the simulation of real life problems requires both a fundamental knowledge in the field of numerical analysis and a proper experience in practical applications as well as ...

    • 1203 - Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws and their Use in Science and Engineering 

      [OWR-2012-5] Workshop Report 2012,5 (2012) - (15 Jan - 21 Jan 2012)
      Modern numerical methods for hyperbolic conservation laws rely on polynomials of high degree, mostly orthogonal polynomials, on triangular or quadrilateral meshes. Due to shocks stability is an issue and modern means of ...

    • 1340 - Uniform Distribution Theory and Applications 

      [OWR-2013-49] Workshop Report 2013,49 (2013) - (29 Sep - 05 Oct 2013)
      The topics of the workshop were recent progress in the theory of uniform distribution theory (also known as discrepancy theory) and new developments in its applications in analysis, approximation theory, computer science, ...