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Node Doubling in Hermite-Gauss Quadrature

Node Doubling in Hermite-Gauss Quadrature. Brian Hagler 2001 http://www.utpb.edu/artsci/faculty/bhagler/research/NodeDoubling.ppt. CONTENTS. Overview Graphics Formulas and Algorithms References. Overview. Hermite Polynomials. Weight Function. Standard Basis. d-Fold Hermite Rationals.

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Node Doubling in Hermite-Gauss Quadrature

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  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

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