1 / 119

Node Doubling in Hermite-Gauss Quadrature

Explore the concept of doubling in Hermite-Gauss quadrature, d-Fold basis, and n-Point formulas with weight functions and polynomials. Graphics, algorithms, and references included.

rcandice
Télécharger la présentation

Node Doubling in Hermite-Gauss Quadrature

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Node Doubling in Hermite-Gauss Quadrature Brian Hagler 2001 http://www.utpb.edu/artsci/faculty/bhagler/research/NodeDoubling.ppt

  2. CONTENTS • Overview • Graphics • Formulas and Algorithms • References

  3. Overview Hermite Polynomials Weight Function Standard Basis

  4. . . . . . . . . .

  5. . . . . . . . . .

  6. d-Fold Hermite Rationals Weight Function Basis

  7. . . .

  8. . . .

  9. d-Fold Doubling . . . . . . . . .

  10. n-Point Hermite-Gauss Quadrature Formula n

  11. 2n

  12. 4n

  13. (2d n)-Point d-FoldHermite-Gauss Quadrature Formula 2dn

  14. Graphicscreated with Mathematica • Hd,n(x) in Bd • Singularities and Quadrature Nodes

  15. Hd,n(x) in Bd n=0 n=1 n=2 . . . d=0 d=1 d=2 . . .

  16. H0,0(x) in B0

  17. H0,1(x) in B0

  18. H0,2(x) in B0

  19. H0,3(x) in B0

  20. H1,0(x) in B1

  21. H1,1(x) in B1

  22. H1,2(x) in B1

  23. H1,3(x) in B1

  24. H1,4(x) in B1

  25. H1,5(x) in B1

  26. H1,6(x) in B1

  27. H2,0(x) in B2

  28. H2,1(x) in B2

  29. H2,2(x) in B2

  30. H2,3(x) in B2

  31. H2,4(x) in B2

  32. H2,5(x) in B2

  33. H2,6(x) in B2

  34. H2,7(x) in B2

  35. H2,8(x) in B2

  36. H2,9(x) in B2

  37. H2,10(x) in B2

  38. H2,11(x) in B2

  39. H2,12(x) in B2

  40. H3,0(x) in B3

  41. H3,1(x) in B3

  42. H3,2(x) in B3

  43. H3,3(x) in B3

More Related