https://www.math.snu.ac.kr/board/files/attach/images/701/ff97c54e6e21a4ae39315f9a12b27314.png
Extra Form
Lecturer 정재훈
Dept. SUNY Buffalo
date Apr 07, 2016

Since Fourier introduced the Fourier series to solve the heat equation, the Fourier or polynomial approximation has served as a useful tool in solving various problems arising in industrial applications. If the function to approximate with the finite Fourier series is smooth enough, the error between the function and the approximation decays uniformly. If, however, the function is nonperiodic or has a jump discontinuity, the approximation becomes oscillatory near the jump discontinuity and the error does not decay uniformly anymore. This is known as the Gibbs-Wilbraham phenomenon. The Gibbs phenomenon is a theoretically well-understood simple phenomenon, but its resolution is not and thus has continuously inspired researchers to develop theories on its resolution. Resolving the Gibbs phenomenon involves recovering the uniform convergence of the error while the Gibbs oscillations are well suppressed. This talk explains recent progresses on the resolution of the Gibbs phenomenon focusing on the discussion of how to recover the uniform convergence from the Fourier partial sum and its numerical implementation. There is no best methodology on the resolution of the Gibbs phenomenon and each methodology has its own merits with differences demonstrated when implemented. This talk also explains possible issues when the methodology is implemented numerically. The talk is intended for a general audience.


  1. Creation of concepts for prediction models and quantitative trading

  2. <학부생을 위한 ɛ 강연> Introduction to the incompressible Navier-Stokes equations

  3. An introduction to hyperplane arrangements

  4. What happens inside a black hole?

  5. <학부생을 위한 ε 강연> Variable-driven sociological research with data innovations

  6. Subword complexity, expansion of real numbers and irrationality exponents

  7. <학부생을 위한 ε 강연> 동형암호와 근사정수론

  8. 4-manifold topology and disk embedding

  9. Hybrid discontinuous Galerkin methods in computational science and engineering

  10. The phase retrieval problem

  11. Theory and applications of partial differential equations

  12. Analysis and computations of stochastic optimal control problems for stochastic PDEs

  13. <학부생을 위한 ε 강연> 압축센싱과 행렬완성

  14. <학부생을 위한 ε 강연> 수학과 예술 - 초기 컴퓨터 그래픽

  15. Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields

  16. Quasi-homomorphisms into non-commutative groups

  17. Entropies on covers of compact manifolds

  18. Iwahori-Hecke algebras and beyond

  19. 15Apr
    by 김수현
    in Math Colloquia

    On the resolution of the Gibbs phenomenon

  20. <학부생을 위한 ε 강연> What mathematics can do for the real and even fake world

Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Next
/ 14