Constrained L2 Degree Reduction by Spline Functions

Scott N. Kersey

Constrained L₂ Degree Reduction by Spline Functions

Scott N. Kersey

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

<div class="line" id="line-21"> Let S0 and S1 be two spaces of polynomial spline curves s : [a,b] → IRd, of order k0 and k1 with k1< k0, defined over knot sequences (ξ0/i) and (ξ1/i), respectively. Fix s0 € S0, and corresponding to each knot ξ 0/I assign a tolerance ǫi ≥ 0. In this paper we present an algorithm for computing the best convex constrained L2 approximant s1 := argmin {&boxv;&boxv;s &boxh;s0 &boxv;&boxv; 2: s € S1 ∩ K} with K := ∩ {s : &boxv;s(t0/i) &boxh; s0 (t 0/i)&boxv; ≤€j}, by the method of alternating projections.</div>

Original language	American English
State	Published - Oct 11 2008
Event	Applied Mathematics and Approximation Theory (AMAT) - Memphis, TN Duration: Oct 11 2008 → …

Conference

Conference	Applied Mathematics and Approximation Theory (AMAT)
Period	10/11/08 → …

Disciplines

Mathematics

Cite this

@conference{5b94069e7ac34c73bf5a8844df74d4cd,

title = "Constrained L2 Degree Reduction by Spline Functions",

abstract = " Let S0 and S1 be two spaces of polynomial spline curves s : [a,b] \→ IRd, of order k0 and k1 with k1< k0, defined over knot sequences (\ξ0/i) and (\ξ1/i), respectively. Fix s0 \€ S0, and corresponding to each knot \ξ 0/I assign a tolerance ǫi \≥ 0. In this paper we present an algorithm for computing the best convex constrained L2 approximant s1 := argmin \{\&boxv;\&boxv;s \&boxh;s0 \&boxv;\&boxv; 2: s \€ S1 \∩ K\} with K := \∩ \{s : \&boxv;s(t0/i) \&boxh; s0 (t 0/i)\&boxv; \≤\€j\}, by the method of alternating projections.",

author = "Kersey, \{Scott N.\}",

year = "2008",

month = oct,

day = "11",

language = "American English",

note = "Applied Mathematics and Approximation Theory (AMAT) ; Conference date: 11-10-2008",

}

TY - CONF

T1 - Constrained L2 Degree Reduction by Spline Functions

AU - Kersey, Scott N.

PY - 2008/10/11

Y1 - 2008/10/11

N2 - Let S0 and S1 be two spaces of polynomial spline curves s : [a,b] → IRd, of order k0 and k1 with k1< k0, defined over knot sequences (ξ0/i) and (ξ1/i), respectively. Fix s0 € S0, and corresponding to each knot ξ 0/I assign a tolerance ǫi ≥ 0. In this paper we present an algorithm for computing the best convex constrained L2 approximant s1 := argmin {&boxv;&boxv;s &boxh;s0 &boxv;&boxv; 2: s € S1 ∩ K} with K := ∩ {s : &boxv;s(t0/i) &boxh; s0 (t 0/i)&boxv; ≤€j}, by the method of alternating projections.

AB - Let S0 and S1 be two spaces of polynomial spline curves s : [a,b] → IRd, of order k0 and k1 with k1< k0, defined over knot sequences (ξ0/i) and (ξ1/i), respectively. Fix s0 € S0, and corresponding to each knot ξ 0/I assign a tolerance ǫi ≥ 0. In this paper we present an algorithm for computing the best convex constrained L2 approximant s1 := argmin {&boxv;&boxv;s &boxh;s0 &boxv;&boxv; 2: s € S1 ∩ K} with K := ∩ {s : &boxv;s(t0/i) &boxh; s0 (t 0/i)&boxv; ≤€j}, by the method of alternating projections.

M3 - Presentation

T2 - Applied Mathematics and Approximation Theory (AMAT)

Y2 - 11 October 2008