Tài liệu Integral Equations and Inverse Theory part 1 pptx

... variable t.790Chapter 18 . Integral Equations and Inverse Theory Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge ... kernel. Equation (18 .0 .1) is analogous to the matrix equationK · f = g (18 .0.2)whose solution is f = K 1 · g,whereK 1 is the matrix inverse. Like equation (18 .0.2), equation (18 .0 .1) has a unique ... http://www.nr.com or call 1- 800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).Chapter 18 . Integral Equations and Inverse Theory 18 .0 IntroductionMany...

Tài liệu Integral Equations and Inverse Theory part 2 docx

... (18 .1. 2) to equation (18 .1. 1), we getf(t)=λNj =1 wjK(t, sj)f(sj)+g(t) (18 .1. 3)Evaluate equation (18 .1. 3) at the quadrature points:f(ti)=λNj =1 wjK(ti,sj)f(sj)+g(ti) (18 .1. 4)Let ... [4]Smithies, F. 19 58, Integral Equations (Cambridge, U.K.: Cambridge University Press).Kanwal, R.P. 19 71, Linear Integral Equations (New York: Academic Press).Green, C.D. 19 69, Integral Equation ... set λ =1/ σ and g =0, then equation (18 .1. 6) becomes a standard eigenvalue equationK ·f = σf (18 .1. 7)which we can solve with any convenient matrix eigenvalue routine (see Chapter 11 ). Note...

Tài liệu Integral Equations and Inverse Theory part 3 ppt

... diag(wj) and its square root,D 1/ 2= diag(√wj). Then equation (18 .1. 7) becomesK · D · f = σfMultiplying by D 1/ 2,wegetD 1/ 2·K·D 1/ 2·h=σh (18 .1. 8)where h = D 1/ 2·f. Equation (18 .1. 8) ... equation (4 .1. 11) :tiaK(ti,s)f(s)ds = h 1 2Ki0f0+i 1 j =1 Kijfj+ 1 2Kiifi (18 .2.3)Thus the trapezoidal method for equation (18 .2 .1) is:f0= g0 (1 − 1 2hKii)fi= ... 794Chapter 18 . Integral Equations and Inverse Theory Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge...

Tài liệu Integral Equations and Inverse Theory part 4 doc

... resultbaw(x)f (x)dx = 1 6f (kh)(k +1) (k+2)(k+3)W0−(3k2 +12 k+ 11 )W 1 +3(k+2)W2−W3+ 1 2f([k +1] h)−k(k+2)(k+3)W0+(3k2 +10 k+6)W 1 −(3k +5)W2+W3+ 1 2f([k +2]h)k(k +1) (k+3)W0−(3k2+8k+3)W 1 +(3k+4)W2−W3+ 1 6f([k ... formula isbaw(x)f(x)dx = 1 2f (kh)(k +1) (k+2)W0−(2k +3)W 1 +W2+f([k +1] h)−k(k+2)W0+2(k +1) W 1 −W2+ 1 2f([k +2]h)k(k +1) W0−(2k +1) W 1 +W2 (18 .3.8)Here the simple special ... zero, then798Chapter 18 . Integral Equations and Inverse Theory Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge...

Tài liệu Integral Equations and Inverse Theory part 5 ppt

... ri(xµ)(xµ +1 − xµ 1 )/2 (18 .4.8)806Chapter 18 . Integral Equations and Inverse Theory Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 ... data,χ2=Ni =1 Nj =1 ci−Mµ =1 Riµu(xµ)S 1 ijcj−Mµ =1 Rjµu(xµ)≈Ni =1 ci−Mµ =1 Riµu(xµ)σi2 (18 .4.9)(compare with equation 15 .1. 5). Here S 1 is the inverse ... 804Chapter 18 . Integral Equations and Inverse Theory Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge...

Tài liệu Integral Equations and Inverse Theory part 6 docx

... = 1 −33 10 0000··· 0− 310 12 6 10 000··· 03 12 19 15 6 10 00··· 0 16 15 20 15 6 10 0··· 00 16 15 20 15 6 10 ··· 0.........0 ··· 0 16 15 20 15 6 10 0··· 00 16 15 20 15 6 1 0 ... = 1 − 210 000··· 0−25− 410 00··· 0 1 −46− 410 0··· 0 01 46− 410 ··· 0.........0 ··· 01 46− 410 0··· 0 01 46− 41 0··· 00 01 45−20··· 000 01 21  (18 .5 .12 ) 18 .5 Linear ... minimizeB∝[u(x)]2dx ∝M−2µ =1 [−uµ+2uµ +1 − uµ+2]2 (18 .5 .10 )implyingB = 12 10 000··· 00 12 10 00··· 0.........0 ··· 000 12 10 0··· 0000 12 1  (18 .5 .11 ) and H = BT·...

Integral Equations and Inverse Theory part 7

... [u( x )] (18 .6 .1) 816 Chapter 18 . Integral Equations and Inverse Theory Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by ... q(x) ·W(x)+λS·q(x) (18 .6 .11 )subject to the constraint (18 .6.7) that q(x) · R =1. The solution of equation (18 .6 .11 ) isq(x)=[W(x)+λS] 1 ·RR·[W(x)+λS] 1 ·R (18 .6 .12 )(Reference[4]gives ... [1] Twomey, S. 19 63,Journal of the Association for Computing Machinery, vol. 10 , pp. 97 10 1. [2]Twomey, S. 19 77,Introduction to the Mathematics of Inversion in Remote Sensing and IndirectMeasurements(Amsterdam:...

Integral Equations and Inverse Theory part 8

... some y the linear system (W(x)+λS)·y =R,andthensubstitute y into both the numerators and denominators of 18 .6 .12 or 18 .6 .13 .) Equations (18 .6 .12 ) and (18 .6 .13 ) have a completely different character ... exp− 1 2χ2exp[−H(u)] (18 .7 .10 )or, equivalently,minimize: − ln [ Prob(u|c)]= 1 2χ2[u]+H(u)= 1 2χ2[u]+Mµ =1 uµln(uµ/U) (18 .7 .11 )This ought to remind you of equation (18 .4 .11 ), ... 818 Chapter 18 . Integral Equations and Inverse Theory Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge...

Tài liệu Improve your ielts writing skill part 1 pptx

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Tài liệu Minimization or Maximization of Functions part 1 pptx

... IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge University Press.Programs Copyright (C) 19 88 -19 92 by Numerical Recipes Software. Permission is ... IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)Copyright (C) 19 88 -19 92 by Cambridge University Press.Programs Copyright (C) 19 88 -19 92 by Numerical Recipes Software. Permission is ... minimum as described in 10 .1, and then use Brent’s method as described in 10 .2. If your functionhas a discontinuous second (or lower) derivative, then the parabolic396Chapter 10 . Minimization or...

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