Recursive construction of optimal smoothing splines with constraints

Fujioka, Hikaru; Kano, Hiroyuki

doi:10.1109/acc.2010.5531592

Cited by 5 publications

(3 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, it has been shown that B-spline approach yielded systematic treatments and solutions for the constrained spline problems using the splines with arbitrary degrees. Moreover, the recursive design algorithm of such constrained splines has recently been developed [14]. But, these methods in [12][13][14] have been applied only when the given data is scalar-valued, and thus we can not impose the constraints cross-coupled among the multiple curves.…”

Section: Introductionmentioning

confidence: 99%

Optimal Vector Smoothing Splines with Coupled Constraints

Fujioka

Kano

2012

Transactions of ISCIE

View full text Add to dashboard Cite

This paper considers the problem of designing optimal vector smoothing spline curves with equality and/or inequality constraints. The constraints are assumed to be cross-coupled among the element curves imposed at some time instant as well as over some time interval. The vector splines are constituted employing normalized uniform B-splines as the basis functions. Then various types of constraints are formulated as linear function of the so-called control points, and the problem is reduced to convex quadratic programming problem. The performance is examined by some numerical examples.

show abstract

Section: Introductionmentioning

confidence: 99%

Optimal Vector Smoothing Splines with Coupled Constraints

Fujioka

Kano

2012

Transactions of ISCIE

View full text Add to dashboard Cite

show abstract

“…Then, it is shown that their construction becomes a quadratic programming problem. Moreover, the recursive design algorithm of such constrained splines has recently been developed [9]. This paper is a continuation of our studies on the optimal design of constrained spline curves based on B-spline approach in [7].…”

Section: Introductionmentioning

confidence: 99%

Optimal Vector Smoothing Splines with Coupled Constraints

Fujioka

Kano

2012

Stochastic Systems Theory and its Applications (SSS)

View full text Add to dashboard Cite

This paper considers the problem of designing optimal smoothing vector spline curves with equality and/or inequality constraints cross-coupled among the element curves. The splines are constituted employing normalized uniform B-splines as the basis functions. Then various types of constraints are formulated as linear function of the so-called control points, and the problem is reduced to convex quadratic programming problem. The performance is examined by some numerical examples.

show abstract

“…We have also developed similar design methods for both the cases of curves and surfaces by employing B-spline approach (Fujioka [2008(Fujioka [ , 2009c). In particular, the design method for the case of curves has recently been extended to the case of constrained splines (Fujioka [2010]).…”

Section: Introductionmentioning

confidence: 99%