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462
Explicit Gaussian quadrature rules for cubic splines with nonuniform knot sequences
"... We provide explicit expressions for quadrature rules on the space of C1 cubic splines with nonuniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that i ..."
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We provide explicit expressions for quadrature rules on the space of C1 cubic splines with nonuniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal
Binary Subdivision Schemes for Functions over Irregular Knot Sequences
 Mathematical Methods in CAGD III
, 1995
"... . For a wide class of stationary subdivision methods, we derive necessary and sufficient conditions for these schemes to produce C k continuous limit curves. These stationary schemes include those arising from midpoint subdivision of irregularlyspaced knot sequences. We also describe a matrix ..."
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Cited by 23 (0 self)
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. For a wide class of stationary subdivision methods, we derive necessary and sufficient conditions for these schemes to produce C k continuous limit curves. These stationary schemes include those arising from midpoint subdivision of irregularlyspaced knot sequences. We also describe a
Odddegree spline interpolation at a biinfinite knot sequence
, 1976
"... It is shown that for an arbitrary strictly increasing knot sequence t =(ti) ∞ − ∞ and for every i, there exists exactly one fundamental spline Li (i.e., Li(tj) =δij, allj), of order 2r whose rth derivative is square integrable. Further, L (r) i (x) is shown to decay exponentially as x moves away f ..."
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Cited by 6 (0 self)
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It is shown that for an arbitrary strictly increasing knot sequence t =(ti) ∞ − ∞ and for every i, there exists exactly one fundamental spline Li (i.e., Li(tj) =δij, allj), of order 2r whose rth derivative is square integrable. Further, L (r) i (x) is shown to decay exponentially as x moves away
WAVELETS CENTERED ON A KNOT SEQUENCE: PIECEWISE POLYNOMIAL WAVELETS ON A QUASICRYSTAL LATTICE
"... Abstract. We develop a general notion of orthogonal wavelets ‘centered ’ on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. As an application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi ..."
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Abstract. We develop a general notion of orthogonal wavelets ‘centered ’ on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. As an application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi
ORTHONORMAL NONUNIFORM BSPLINE SCALING AND WAVELET BASES ON NONEQUALLY SPACED KNOT SEQUENCE FOR MULTIRESOLUTION SIGNAL APPROXIMATIONS
"... This paper investigates the mathematical framework of multiresolution analysis based on irregularly spaced knots sequence. Our presentation is based on the construction of nested nonuniform Bspline multiresolution spaces. From these spaces, we present the construction of orthonormal scaling and wa ..."
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Cited by 1 (0 self)
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This paper investigates the mathematical framework of multiresolution analysis based on irregularly spaced knots sequence. Our presentation is based on the construction of nested nonuniform Bspline multiresolution spaces. From these spaces, we present the construction of orthonormal scaling
Selecting the Number of Knots For Penalized Splines
, 2000
"... Penalized splines, or Psplines, are regression splines fit by leastsquares with a roughness penaly. Psplines have much in common with smoothing splines, but the type of penalty used with a Pspline is somewhat more general than for a smoothing spline. Also, the number and location of the knots ..."
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Cited by 105 (10 self)
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sequence of possible numbers of knots and chooses the candidate that minimizes GCV. The myoptic algo...
Sequences of Knots and Their Limits
, 801
"... Abstract. Hyperfinite knots, or limits of equivalence classes of knots induced by a knot invariant taking values in a metric space, were introduced in a previous article by the author. In this article, we present new examples of hyperfinite knots stemming from sequences of torus knots. ..."
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Abstract. Hyperfinite knots, or limits of equivalence classes of knots induced by a knot invariant taking values in a metric space, were introduced in a previous article by the author. In this article, we present new examples of hyperfinite knots stemming from sequences of torus knots.
UNKNOTTING SEQUENCES FOR TORUS KNOTS
, 2008
"... The unknotting number of a knot is bounded from below by its slice genus. It is a wellknown fact that the genera and unknotting numbers of torus knots coincide. In this note we characterize quasipositive knots for which the genus bound is sharp: the slice genus of a quasipositive knot equals its ..."
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unknotting number, if and only if the given knot appears in an unknotting sequence of a torus knot.
Maximum Knotted Switching Sequences
, 2008
"... In this paper, we define the maximum knotted switching sequence length of a knot projection and investigate some of its properties. In particular, we examine the effects of Reidemeister and flype moves on maximum knotted switching sequences, show that every knot has projections having a full seque ..."
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In this paper, we define the maximum knotted switching sequence length of a knot projection and investigate some of its properties. In particular, we examine the effects of Reidemeister and flype moves on maximum knotted switching sequences, show that every knot has projections having a full
Knot Removal for BSpline Curves
, 1994
"... In the present paper the problem of removing one inner knot from the knot sequence of a Bspline curve is discussed. Doing so, a local (geometric) construction of the new control points from the given ones is first introduced. Then the degrees of freedom appearing in this general construction are de ..."
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Cited by 14 (1 self)
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In the present paper the problem of removing one inner knot from the knot sequence of a Bspline curve is discussed. Doing so, a local (geometric) construction of the new control points from the given ones is first introduced. Then the degrees of freedom appearing in this general construction
Results 1  10
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462