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We easily evaluate the Valoe sg the fla at t0, Xx Xe, fo fi fa ana" t- t Grx +9o. PG) = do C6) fGc-1) + 2e(a) flan) + 2a6) f(ori t) . Thin fonction distinct points. n+1 fn. PG) %3D %3D Pl) = fo Lo(2) +fiLia) the L.(1) +f Lo(@) He would heve %3D P(Xx) =fK for k=0,..,n. Where p(Xx) is our nth Lagnange interpulating folynomiel. The fonchton fle) i's in the mplacement grin by EnCxit) = fa)- Plx). and it Vaulne from Point to point. replaced Ly the Polynomigl pce) , the error mcde Blynomigl P(e) , the eror me, iš givin by %3D For 3 points we heve nニ 4G)= La(a) So %3D

We easily evaluate the Valoe sg the fla at t0, Xx Xe, fo fi fa ana" t- t Grx +9o. PG) = do C6) fGc-1) + 2e(a) flan) + 2a6) f(ori t) . Thin fonction distinct points. n+1 fn. PG) %3D %3D Pl) = fo Lo(2) +fiLia) the L.(1) +f Lo(@) He would heve %3D P(Xx) =fK for k=0,..,n. Where p(Xx) is our nth Lagnange interpulating folynomiel. The fonchton fle) i's in the mplacement grin by EnCxit) = fa)- Plx). and it Vaulne from Point to point. replaced Ly the Polynomigl pce) , the error mcde Blynomigl P(e) , the eror me, iš givin by %3D For 3 points we heve nニ 4G)= La(a) So %3D

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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We easily exaloate the Yalues g the eYaluate the Valops og the fonction fla) at ntl distinct points. to, Xx Xz,) Xn fo fi fa PG) = ana" +- t91x +90. PG) = do o)f Gi-1)+2efa) flear) +2a6) flxiti). Thin Pla) = fo Loca) tfilica) He would heve the L=(x) +fs La(). %3D PCXK)=fK for k=0,. in. Wherne g folynoniel. P(Xx)is our nth Lagrange interpolating fonction fle) in the moplacement Enlxif) = The is ruplaced Ly the Rlynomial Ple), the enor mcde is givin by fe)-P). and it Vaulne from Point to point. For 3 3 pojnts we hcro points 4@= x(x-I) (a-2) (x-x) 40) %3D La(a) So 2. %3D
Transcribed Image Text:We easily exaloate the Yalues g the eYaluate the Valops og the fonction fla) at ntl distinct points. to, Xx Xz,) Xn fo fi fa PG) = ana" +- t91x +90. PG) = do o)f Gi-1)+2efa) flear) +2a6) flxiti). Thin Pla) = fo Loca) tfilica) He would heve the L=(x) +fs La(). %3D PCXK)=fK for k=0,. in. Wherne g folynoniel. P(Xx)is our nth Lagrange interpolating fonction fle) in the moplacement Enlxif) = The is ruplaced Ly the Rlynomial Ple), the enor mcde is givin by fe)-P). and it Vaulne from Point to point. For 3 3 pojnts we hcro points 4@= x(x-I) (a-2) (x-x) 40) %3D La(a) So 2. %3D
Evaluating the deivative g The interpolating functiun at Xx= h. formula for the Second deivative interpoletion Contral difference g fe) at Xi using quadate Laq range Pla) = Solution Intorpoleting functon = fle) p? (ari) =f2-2fi+ fo %31 For a difference formula for fi, I we need ptl nodes for o(n) occumence and ptN nodes for oCh) occuracy Contral approscimetions for even order derivatives require fewer nodes due to a fortunate Cancelation g eror terms pla) must match fcac) at the P( kle have P(as) = foVo(d3) +fiVi (as) +fe Vz(93) U sing the definition for . pla) as Selected data points. 3 intrpolation Points. 131 Li0)flai-)+ 22(x)f(ai)+ 23(x)fxiti). We assume That. P(as) = floxs) Degne N. Poota at do,Xi,Xz;.- Xc-1,litt,.XN (at all nodew eXcept Xi) ViCxi) = 1. Let Hila) = (x-x0) (x-a)(x-x2) -... (a-xi-) ( -xi+1) . (x- Xn) He noimalize Hila) and detine the Lagiangu We Construct Yila). %3D %3D basiv function (ai-00)i-2)(-aa) - (ai-odi-) Gi-aial).i-N) P(a) = fo X-a)(a-)-2) %3D 十和 th +fa (x- X) (x-1)(2-2) fx-x0)(x-1)(-13)
Transcribed Image Text:Evaluating the deivative g The interpolating functiun at Xx= h. formula for the Second deivative interpoletion Contral difference g fe) at Xi using quadate Laq range Pla) = Solution Intorpoleting functon = fle) p? (ari) =f2-2fi+ fo %31 For a difference formula for fi, I we need ptl nodes for o(n) occumence and ptN nodes for oCh) occuracy Contral approscimetions for even order derivatives require fewer nodes due to a fortunate Cancelation g eror terms pla) must match fcac) at the P( kle have P(as) = foVo(d3) +fiVi (as) +fe Vz(93) U sing the definition for . pla) as Selected data points. 3 intrpolation Points. 131 Li0)flai-)+ 22(x)f(ai)+ 23(x)fxiti). We assume That. P(as) = floxs) Degne N. Poota at do,Xi,Xz;.- Xc-1,litt,.XN (at all nodew eXcept Xi) ViCxi) = 1. Let Hila) = (x-x0) (x-a)(x-x2) -... (a-xi-) ( -xi+1) . (x- Xn) He noimalize Hila) and detine the Lagiangu We Construct Yila). %3D %3D basiv function (ai-00)i-2)(-aa) - (ai-odi-) Gi-aial).i-N) P(a) = fo X-a)(a-)-2) %3D 十和 th +fa (x- X) (x-1)(2-2) fx-x0)(x-1)(-13)
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