View source for Hyperbolic Spline Interpolation

{{DISPLAYTITLE:Hyperbolic Spline Interpolation (Hyperbolic Spline Interpolation)}}
== Description == 

The problem of restoring complex curves and surfaces from discrete data so that their shape is preserved is called isogeometric interpolation. A very popular tool for solving this problem are hyperbolic splines in tension, which were introduced in 1966 by Schweikert. These splines have smoothness sufficient for many applications; combined with algorithms for the automatic selection of the tension parameters, they adapt well to the given data. Unfortunately, the evaluation of hyperbolic splines is a very difficult problem because of roundoff errors (for small values of the tension parameters) and overflows (for large values of these parameters).�

== Parameters == 

$n$: number of points

== Table of Algorithms == 

{| class="wikitable sortable"  style="text-align:center;" width="100%"

! Name !! Year !! Time !! Space !! Approximation Factor !! Model !! Reference

|-

| [[B.I. Kvasov (Hyperbolic Spline Interpolation Hyperbolic Spline Interpolation)|B.I. Kvasov]] || 2008 || $O(n^{3} \log^{2}K)$ || $O(n)$? || Exact || Deterministic || [https://link.springer.com/article/10.1134/S0965542508040039 Time]
|-
| [[V. A. Lyul’ka and A. V. Romanenko (Hyperbolic Spline Interpolation Hyperbolic Spline Interpolation)|V. A. Lyul’ka and A. V. Romanenko]] || 1994 || $O(n^{5})$ ||  || Exact || Deterministic || [https://www.mathnet.ru/eng/zvmmf2544 Time]
|-
| [[V. A. Lyul’ka and I. E. Mikhailov (Hyperbolic Spline Interpolation Hyperbolic Spline Interpolation)|V. A. Lyul’ka and I. E. Mikhailov]] || 2003 || $O(n^{4})$ ||  || Exact || Deterministic || [http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=zvmmf&paperid=943&option_lang=eng Time]
|-
| [[V. I. Paasonen (Hyperbolic Spline Interpolation Hyperbolic Spline Interpolation)|V. I. Paasonen]] || 1968 || $O(n^{5} \log K)$ ||  || Exact || Deterministic ||  
|-
| [[P. Costantini, B. I. Kvasov, and C. Manni (Hyperbolic Spline Interpolation Hyperbolic Spline Interpolation)|P. Costantini, B. I. Kvasov, and C. Manni]] || 1999 || $O(n^{5} \log K)$ || $O(n)$? || Exact || Deterministic || [https://link.springer.com/article/10.1023/A:1018988312596 Time]
|-
| [[B. I. Kvasov (Hyperbolic Spline Interpolation Hyperbolic Spline Interpolation)|B. I. Kvasov]] || 2000 || $O(n^{4})$ || $O(n)$?? || Exact || Deterministic || [http://sutir.sut.ac.th:8080/sutir/bitstream/123456789/431/1/bib115.pdf Time]
|-
|}

== Time Complexity Graph == 

[[File:Hyperbolic Spline Interpolation - Time.png|1000px]]