curve fitting and interpolation

Ngày tải lên: 14/03/2014, 19:33

... relative flat knot and the nonresonance condition Let Γ = {γ1 , , γN } ⊂ Ω be a collection of curves with no mutual CURVE SHORTENING AND GEODESICS 1191 or self-tangencies, and denote by MΓ the ... construction to curve shortening, and which results could be obtained in this way This turned out to be a very fruitful question, even though in the CURVE SHORTENING AND GEODESICS 1193 end curve shortening ... satellites and Poincar´’s e rotation number 1.1 Satellites Let α ∈ Ω be given, and let α : R/Z → M also denote a constant speed parametrization of α Choose a unit normal N along α, and consider the curve...

Ngày tải lên: 29/03/2014, 07:20

... N the denominator in the right–hand side vanishes) On the other hand, the expression in the right–hand side of (1.14) is a particular case of that in the right–hand side of (1.13): here π is the ... projection, can be defined as follows: if s, s1 , s2 ∈ S(n − 1) and (n − 1, n) stands for the elementary transposition of “n − 1” and “n”, then s → s and s1 · (n − 1, n) · s2 → s1 s2 In other words, the ... (7.1) λ∈Gn Indeed, take (7.1) and (7.2) as the definition of the functions ϕ ∨ ψ and ϕ ∧ ψ For any fixed µ, the sum in the right–hand side of (7.1) increases as n → ∞ and remains bounded from above...

Ngày tải lên: 07/08/2014, 06:20

... contributions JS analyzed and interpreted the patient data regarding the hospital progress and rehabilitation AA supervised the prosthetic fitting and rehabilitation AA and SS were major contributors ... not considered candidates for prosthetic fitting and rehabilitation However, we describe a case of a 67-year-old woman with severe COPD who was fitted with a lower-limb prosthesis and successfully ... rehabilitation program included general upper- and lower-extremity strengthening and conditioning exercises Oxygen supplementation during exercise and ambulation greatly facilitated the rehabilitation...

Ngày tải lên: 11/08/2014, 02:22

... problems (specific cases of the general interpolation problem) Taylor interpolation problem, Lagrange interpolation problem, Newton interpolation problem and Hermite interpolation problem ∙ In the last ... operators (specific cases of the general interpolation problem) Taylor interpolation problem, Lagrange interpolation problem, Newton interpolation problem and Hermite interpolation problem Chapter 3, ... Elements Cx and Sx are said to be cosine and sine elements The mappings C and S are said to be cosine and sine mappings (trigonometric mappings) We can see that trigonometric mappings and elements...

Ngày tải lên: 21/03/2015, 22:59

... (Keller and Massart, 1991), and HELP (Kvalheim and Liang, 1992; Liang et al., 1992; Keller et al., 1992; Liang and Kvalheim, 2001) Among these methods, WFA and HELP are probably the most studied and ... Zhang Huajun and Dr Srilakshmi Chilukoti for their friendship, enriching conversation and help in the past four and half years My deepest gratitude goes to my family for their love and care through ... ultra-violet circular dichroism (UV CD) and Raman Optical Activity (ROA), and Far-IR and Far-Raman spectroscopy This thesis focuses on solving the qualitative and quantitative analysis of multivariate...

Ngày tải lên: 12/09/2015, 08:20

... closed curves, where t parameterizes the family and p parameterizes the curve 2.1 Curve evolution and Level set representation of curve evolution Definition 2.1.1 We say that C(p, t) is a curve ... Geometric Curves iv Contents v 2.1 Curve evolution and Level set representation of curve evolution 2.2 Curve shortening 17 2.3 Geometric Heat Flow and Preservation ... this chapter, we use sources [Gage1], [Gage2] and [Sapiro & Tannenbaum] 2.1 Curve evolution and Level set representation of curve evolution We consider curves that deform over time We let C(p, t)...

Ngày tải lên: 04/10/2015, 10:24

... Ball, Laurence, and Robert Moffit (2001) "Productivity Growth and the Phillips Curve, " NBER Working Paper No 8421 [8] Blackaby, David H., and Lester C Hunt (1992) "The "Wage Curve" and Long-Term ... the standard model at both, the one-year and two-year horizons, and for all three specifications of the Phillips Curve This is reflected on the lower RMSE values (improvement over the standard ... synthetic euro area data are used to estimate the standard and modified models of the Phillips Curve The main results are presented in Tables and 5, and Figure Estimation values show that the coefficient...

Ngày tải lên: 24/10/2012, 09:11

... of the function better than spline Polynomial multiplication and division (convolution and deconvolution) are performed by the conv and deconv functions MATLAB also has a built-in fast Fourier ... closed form, and the last example cannot be solved by int at all It can only be computed numerically, with quad 121 The function f provided to quad and quadl must operate on a vector x and return ... of the vector An optional fourth argument to quad and quadl modifies the error tolerance Double and triple integrals are evaluated by dblquad and triplequad Arrayvalued functions are integrated...

Ngày tải lên: 29/09/2013, 22:20

... through m and (the term R(i+1) (i+m−1) in equation 3.2.3) m−1 points It is started with (3.2.4) Ri = yi and with (3.2.5) R ≡ [Ri(i+1) (i+m) with m = −1] = Now, exactly as in equations (3.1.4) and (3.1.5) ... ya[], int n, float x, float *y, float *dy) Given arrays xa[1 n] and ya[1 n], and given a value of x, this routine returns a value of y and an accuracy estimate dy The value returned is that of the ... trade@cup.cam.ac.uk (outside North America) x−xi x−xi+m 3.3 Cubic Spline Interpolation 113 } CITED REFERENCES AND FURTHER READING: Stoer, J., and Bulirsch, R 1980, Introduction to Numerical Analysis (New...

Ngày tải lên: 17/10/2013, 22:15

... 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 y is ... 114 Chapter Interpolation and Extrapolation where A≡ xj+1 − x xj+1 − xj B ≡ 1−A = x − xj xj+1 − xj (3.3.2) y = Ayj + Byj+1 + Cyj + Dyj+1 (3.3.3) where A and B are defined in (3.3.2) and C≡ (A − ... interval, and an undefined, or infinite, second derivative at the abscissas xj The goal of cubic spline interpolation is to get an interpolation formula that is smooth in the first derivative, and continuous...

Ngày tải lên: 20/10/2013, 17:15

... supply much shorter xx and yy arrays, of length m How you make the connection? The solution: Calculate k = IMIN(IMAX(j-(m-1)/2,1),n+1-m) (The macros IMIN and IMAX give the minimum and maximum of two ... §1.2 and Appendix B.) This expression produces the index of the leftmost member of an m-point set of points centered (insofar as possible) between j and j+1, but bounded by at the left and n ... lets you call the interpolation routine with array addresses offset by k, e.g., polint(&xx[k-1],&yy[k-1],m, ) CITED REFERENCES AND FURTHER READING: Knuth, D.E 1973, Sorting and Searching, vol...

Ngày tải lên: 20/10/2013, 17:15

... x2a[k])/(x2a[k+1] − x2a[k]) (3.6.4) (so that t and u each lie between and 1), and y(x1 , x2) = (1 − t)(1 − u)y1 + t(1 − u)y2 + tuy3 + (1 − t)uy4 (3.6.5) Bilinear interpolation is frequently “close enough ... free_vector(x,0,n); 123 3.6 Interpolation in Two or More Dimensions 3.6 Interpolation in Two or More Dimensions ya[j][k] = y(x1a[j], x2a[k]) (3.6.1) We want to estimate, by interpolation, the function ... x2a[k+1] (3.6.2) defines j and k, then y1 ≡ ya[j][k] y2 ≡ ya[j+1][k] y3 ≡ ya[j+1][k+1] (3.6.3) y4 ≡ ya[j][k+1] The simplest interpolation in two dimensions is bilinear interpolation on the grid...

Ngày tải lên: 24/10/2013, 15:15

... arrays x1a[1 m] and x2a[1 n] of independent variables, and a submatrix of function values ya[1 m][1 n], tabulated at the grid points defined by x1a and x2a; and given values x1 and x2 of the independent ... taste (and trade-off between time and memory) as to how much of this process one wants to precompute and store Instead of precomputing and storing all the derivative information (as in bicubic interpolation) , ... gradients, and cross derivative at the four grid points of a rectangular grid cell (numbered counterclockwise from the lower left), and given d1 and d2, the length of the grid cell in the 1- and 2-directions,...

Ngày tải lên: 07/11/2013, 19:15

... Chapter Interpolation and Extrapolation f(x, y, z) Multidimensional interpolation is often accomplished by a sequence of one-dimensional interpolations We discuss this in §3.6 CITED REFERENCES AND ... (minus one) used in an interpolation scheme is called the order of the interpolation Increasing the order does not necessarily increase the accuracy, especially in polynomial interpolation If the ... the desirable order of interpolation, you must begin each interpolation with a search for the right “local” place in the table While not strictly a part of the subject of interpolation, this task...

Ngày tải lên: 21/01/2014, 18:20

... 4-point interpolation on the tabulated values xx[15 18], yy[15 18] For more on this, see the end of §3.4 CITED REFERENCES AND FURTHER READING: Abramowitz, M., and Stegun, I.A 1964, Handbook of ... free_vector(d,1,n); free_vector(c,1,n); 3.2 Rational Function Interpolation and Extrapolation 111 3.2 Rational Function Interpolation and Extrapolation Ri(i+1) (i+m) = p + p1 x + · · · + pµ x µ ... (outside North America) P23 110 Chapter Interpolation and Extrapolation float *c,*d; } Quite often you will want to call polint with the dummy arguments xa and ya replaced by actual arrays with...

Ngày tải lên: 26/01/2014, 15:20

... instruments used by banks and other financial instruments to manage their credit risk exposure, and as such is a credit derivative They are used as credit risk management tools, and also as synthetic ... product and therefore a credit derivative An investor may wish to receive such cash flows synthetically for tax, accounting, regulatory capital, external audit or legal reasons On the other hand, ... difference between the initial market value and any depreciation, so it is sometimes termed the ‘guarantor’ while Bank A is the ‘beneficiary’ ©YieldCurve.com 2004 Page Bank A Total Return payer...

Ngày tải lên: 15/02/2014, 14:20

... integer and a point on an elliptic curve [16] 3.2 Elliptic curve over finite field Fq Fundamental theory Elliptic curve can be defined over finite field Fq with q = p or q = 2m, that m and p are ... with a prime p and Fq m with q = p r With p = 2, all operators can be easily carried out on the devices Operation over curves includes addition of points on an elliptic curve and scalar multiplication ... to solve under defined elliptic curve above We have H : {0,1}* → Zq* is a hash Let E be an elliptic curve over a finite field Fq , and G ∈ E Fq a point of order n and Registration server RS picks...

Ngày tải lên: 14/03/2014, 10:20

... Grossman and Krueger (1991), Shafik and Bandyopadhyay (1992), Panayotou (1993), Selden and Song (1994), and Holtz-Eakin and Selden (1995) Special issues of Ecological Economics (1995, 1998) and Environment ... Environmental Kuznets Curves? Journal of Environmental Planning and Management 43, 139-153 McConnell, K.E., 1997 Income and the demand for environmental quality Environment and Development Economics ... Van den Bergh (Editor) Handbook of Environmental and Resource Economics Edward Edgar Cheltenham, UK, pp 656-677 Ekins, P., 1997 The Kuznets curve for the environment and economic growth: examining...

Ngày tải lên: 15/03/2014, 16:20