Interpolation and Extrapolation part 3

... started with R i = y i (3. 2.4) and with R ≡ [R i(i+1)...(i+m) with m = −1] = 0 (3. 2.5) Now, exactly as in equations (3. 1.4) and (3. 1.5) above, we can convert the recurrence (3. 2 .3) to one involving ... NJ: Prentice-Hall), § 6.2. Cuyt, A., and Wuytack, L. 1987, Nonlinear Methods in Numerical Analysis (Amsterdam: North- Holland), Chapter 3. 3. 3 Cubic Spline Interpolation Given a tabulated function ... ),i=1...N, focus attention on one particular interval, between x j and x j+1 . Linear interpolation in that interval gives the interpolation formula y = Ay j + By j+1 (3. 3.1) ...

... replacing (3. 3.1) byy = Ayj+ Byj+1+ Cyj+ Dyj+1 (3. 3 .3) where A and B are defined in (3. 3.2) and C ≡16(A 3 − A)(xj+1− xj)2D ≡16(B 3 − B)(xj+1− xj)2 (3. 3.4)Notice ... attention on oneparticular interval, between xj and xj+1. Linear interpolation in that interval givesthe interpolation formulay = Ayj+ Byj+1 (3. 3.1)114Chapter 3. Interpolation and Extrapolation Sample ... independent variable x in equations (3. 3 .3) and (3. 3.4) is entirely through the linear x-dependence of A and B, and (through A and B) the cubic x-dependence of C and D.We can readily check that...

... see in Chapter 16, call118Chapter 3. Interpolation and Extrapolation Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by ... call 1-800-872-74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).hunt phasebisection phase1710814 22 32 38 32 1(a)(b)5164Figure 3. 4.1. (a) The ... 1-800-872-74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America). 3. 4 How to Search an Ordered TableSuppose that you have decided to use some particular interpolation...

... 120Chapter 3. Interpolation and Extrapolation Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by ... xNN·c0c1...cN=y0y1...yN (3. 5.2)This is a Vandermonde matrix, as described in §2.8. One could in principle solveequation (3. 5.2) by standardtechniquesfor linearequationsgenerally(§2 .3) ; howeverthe special ... k,j,i;float xmin,dy,*x,*y;122Chapter 3. Interpolation and Extrapolation Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by...

... 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, -3, 0,0 ,3, 0,0,0,0,-2,0,0,-1,0,0,0,0,2,0,0,-2,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, -3, 0,0 ,3, 0,0,0,0,-2,0,0,-1,0,0,0,0,2,0,0,-2,0,0,0,0,1,0,0,1, -3, 3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, -3, 3,0,0,-2,-1,0,0,9,-9,9,-9,6 ,3, -3, -6,6,-6, -3, 3,4,2,1,2,-6,6,-6,6,-4,-2,2,4, -3, 3 ,3, -3, -2,-1,-1,-2,2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0,-6,6,-6,6, -3, -3, 3 ,3, -4,4,2,-2,-2,-2,-1,-1,4,-4,4,-4,2,2,-2,-2,2,-2,-2,2,1,1,1,1};int ... 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, -3, 0,0 ,3, 0,0,0,0,-2,0,0,-1,0,0,0,0,2,0,0,-2,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0, -3, 0,0 ,3, 0,0,0,0,-2,0,0,-1,0,0,0,0,2,0,0,-2,0,0,0,0,1,0,0,1, -3, 3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, -3, 3,0,0,-2,-1,0,0,9,-9,9,-9,6 ,3, -3, -6,6,-6, -3, 3,4,2,1,2,-6,6,-6,6,-4,-2,2,4, -3, 3 ,3, -3, -2,-1,-1,-2,2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0,-6,6,-6,6, -3, -3, 3 ,3, -4,4,2,-2,-2,-2,-1,-1,4,-4,4,-4,2,2,-2,-2,2,-2,-2,2,1,1,1,1};int ... wanders from grid square to grid square, the interpolated124Chapter 3. Interpolation and Extrapolation Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright...

... otherwise takes on all positive and negative values. Any interpolation basedon the values x =3. 13, 3. 14, 3. 15, 3. 16, will assuredly get a very wrong answer forthe value x =3. 1416, even though a graph ... functionf(x)=3x2+1π4ln(π − x)2+1 (3. 0.1)105106Chapter 3. Interpolation and Extrapolation Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright ... http://www.nr.com or call 1-800-872-74 23 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).Chapter 3. Interpolation and Extrapolation 3. 0 IntroductionWesometimesknowthevalueofafunctionf(x)...

... right. For example, with N =4,x1: y1=P1P12x2: y2= P2P1 23 P 23 P1 234 x 3 : y 3 = P 3 P 234 P 34 x4: y4= P4 (3. 1.2)Neville’s algorithm is a recursive way of filling in the numbers ... higher-orderpolynomials, up toP1 23 N, which is the valueof the unique interpolatingpolynomialthrough all N points, i.e., the desired answer. 3. 1 Polynomial Interpolation and Extrapolation 109Sample ... 108Chapter 3. Interpolation and Extrapolation Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521- 431 08-5)Copyright (C) 1988-1992 by...

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... Negative input timing constraints can also be specified. 10 .3. 1 $setup and $hold Checks $setup and $hold tasks are used to check the setup and hold constraints for a sequential element in the design. ... converted to layout by a place and route tool. The post-layout delay values are computed from the resistance (R) and capacitance (C) information in the layout. The R and C information is extracted ... checked for violations //Violation reported if Tposedge_clk - Tdata < 3 specify $setup(data, posedge clock, 3) ; endspecify $hold task Hold checks can be specified with the system task...