PDF Publication Title:
Text from PDF Page: 111
For r ≤ 1, (4.29) gives E[AN+2] = rN+2 Γ(b + N + 3)Γ(a + b + 2) Γ(b+1)Γ(a+b+N +4) 4.7 ⋅ algorithm analysis 89 = rN+2 Γ(a + b + 2) Γ(b+1) 1 (b+N +3)(b+N +4)⋯(a+b+N +3) (4.40) ≤ rN+2 Γ(a + b + 2) 1 , Γ(b+1) (b+N+3)a+1 from which we conclude that the path damping algorithm for computing N+2 E [x(A)] converges like N a+1 . 4.7.3 Error bounds on Gaussian quadrature Quadrature methods are extremely old tools and many excellent error analysis techniques exist. For example, Davis and Rabinowitz [1984] devotes anentirechaptertotheirstudy.LetxGQ(N) betheapproximationtoE[x(A)] using an N-point quadrature rule. We can only achieve an error bound for any component and thus use the upper bound ∥E [x(A)] − xGQ(N)∥ ≤ n ∣E [x (A)] − xGQ(N)∣ . r This bound is terrible for large n and we do not expect it to be tight. Instead, we focus on the error decay—how much the error drops when N. Computing the bound on a component is involved, as the following theo- rem and proof demonstrate. Theorem 14. Let A be a random variable with finite moments and support [0, r], where r < 1. The error in the Gauss quadrature approximation of E [x(A)] is bounded above by 32ωr ∣E[xi(A)]−xi ∣≤ −2 2N+2 , 15(1 − ρ )ρ where N is the number of points in the Gauss quadrature rule, √√ 111 ω= 1+ and ρ= + −1. r rr2 GQ(N) i iPDF Image | Instagram Cheat Sheet
PDF Search Title:
Instagram Cheat SheetOriginal File Name Searched:
pagerank-sensitivity-thesis-online.pdfDIY PDF Search: Google It | Yahoo | Bing
Cruise Ship Reviews | Luxury Resort | Jet | Yacht | and Travel Tech More Info
Cruising Review Topics and Articles More Info
Software based on Filemaker for the travel industry More Info
The Burgenstock Resort: Reviews on CruisingReview website... More Info
Resort Reviews: World Class resorts... More Info
The Riffelalp Resort: Reviews on CruisingReview website... More Info
| CONTACT TEL: 608-238-6001 Email: greg@cruisingreview.com | RSS | AMP |