Displaying similar documents to “Approximation by circular splines for solutions of ordinary differential equations”

Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey

Vladimir Bogdanov, Wladimir Karsten, Valeriy Miroshnichenko, Yuriy Volkov (2013)

Open Mathematics

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A method for solving the inverse kinematic problem of determining the velocity characteristic of a medium from a vertical seismic survey, is proposed. It is based on the combined use of the eikonal equation and spline methods of approximation for multivariable functions. The problem is solved by assuming a horizontally stratified medium; no assumptions about the number of layers and their thickness are made. First, using the data of the first arrival times of the seismic signal from...

Interpolating and smoothing biquadratic spline

Radek Kučera (1995)

Applications of Mathematics

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The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic...

A note on tension spline

Segeth, Karel

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Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the...

Quadratic splines smoothing the first derivatives

Jiří Kobza (1992)

Applications of Mathematics

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The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights w i and smoothing parameter α , is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter α is mentioned.

Chebyshevian splines

Zygmunt Wronicz

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CONTENTSIntroduction...........................................................................................................5I.   Canonical complete Chebyshev systems   1. Canonical complete Chebyshev systems.......................................................7   2. Interpolation by generalized polynomials and divided differences................12   3. The Markov inequality for generalized polynomials......................................16II.   Chebyshevian splines   1. Basic...