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Lacunary Interpolation by Splines
SIAM Journal on Numerical Analysis, 1973In 1955, J. Suranyi and P. Turan commenced the study of what they called (0,2) interpolation. By (0,2) interpolation we mean the problem of finding the algebraic polynomial of degree ≤ 2n-1, if it exists, whose values and second derivatives are prescribed on n given nodes.
Meir, A., Sharma, A.
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Interpolation by Bilinear splines
Mathematical Notes of the Academy of Sciences of the USSR, 1990Let \(\Omega=[0,1]\times[0,1]\) and let \(C^{1,1}_ \omega(\Omega)\) denote a space of bivariate functions with continuous partial derivatives of order one on \(\Omega\) with \(\omega(f;t,\tau)\leq\omega(t,\tau)\). Here, \(\omega(t,\tau)\) denotes a convex modulus of continuity and \(\omega(f;t,\tau)\) stands for the usual modulus of continuity of \(f\).
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Forward Stabilized Spline Interpolation
SIAM Journal on Control and Optimization, 2006Forward interpolation, as discussed in the article, refers to the problem of interpolating data points revealed, one at a time, in a sequential manner. Forward spline interpolation is an inherently unstable process. The stability does not obtain automatically; it needs to be designed into the process using system theoretic tools.
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IMA Journal of Numerical Analysis, 1984
A cubic X-spline with knots \(\{x_ i\}^ N_{i=0}\) and parameter vector \(\{c_ i\}\) is a function \(s\in C^ 1[a,b]\) if \[ (i)\quad s(x)\text{ is a cubic on each } [x_{i-1},x_ i], \] \[ (ii)\quad s'(a)=[s(x_ 1)-s(x_ 0)]/h_ 1\text{ and } s'(b)=[s(x_ N)-s(x_{N- 1})]/h_ n, \] and \[ (iii)\quad s^{(2)}(x_ i+)-s^{(2)}(x_ i- )=(c_ ih_{i+1}/3)[s^{(3)}(x_ i ...
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A cubic X-spline with knots \(\{x_ i\}^ N_{i=0}\) and parameter vector \(\{c_ i\}\) is a function \(s\in C^ 1[a,b]\) if \[ (i)\quad s(x)\text{ is a cubic on each } [x_{i-1},x_ i], \] \[ (ii)\quad s'(a)=[s(x_ 1)-s(x_ 0)]/h_ 1\text{ and } s'(b)=[s(x_ N)-s(x_{N- 1})]/h_ n, \] and \[ (iii)\quad s^{(2)}(x_ i+)-s^{(2)}(x_ i- )=(c_ ih_{i+1}/3)[s^{(3)}(x_ i ...
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Efficient spline interpolation
Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers, 2002The problem of interpolating data points using a smooth function has many existing solutions. In particular, the use of piecewise polynomials (splines) has provided solutions with user controlled smoothness. In this paper we introduce a new interpolation procedure which utilizes multiple knot Hermitian splines.
L.A. Ferrari, P.V. Sankar
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Comonotone Adaptive Interpolating Splines
BIT Numerical Mathematics, 2002The paper deals with the construction of \(C^1\) interpolating spline with either a quadratic polynomial or a linear/linear rational function between the knots. Such spline preserves the monotonicity of the data on the rational sections. The author proves the existence and the uniqueness of the spline above defined and proposes numerical examples ...
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Lacunary Polynomial Spline Interpolation
SIAM Journal on Numerical Analysis, 1976A special form of the Birkhoff interpolation problem is investigated. We prove an existence theorem for certain types of interpolation which, in a particular case, reduces to a theorem of Meir and Sharma for $(0,2)$ interpolation by $C^3 $ piecewise quintics.
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Mathematical Notes of the Academy of Sciences of the USSR, 1979
Malozemov, V. N., Pevnyj, A. B.
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Malozemov, V. N., Pevnyj, A. B.
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Geodesic Interpolating Splines
2001We propose a simple and efficient method to interpolate landmark matching by a non-ambiguous mapping (a diffeomorphism). This method is based on spline interpolation, and on recent techniques developed for the estimation of flows of diffeomorphisms. Experimental results show interpolations of remarkable quality.
Vincent Camion, Laurent Younes
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