{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T12:11:56Z","timestamp":1725451916241},"reference-count":0,"publisher":"EasyChair","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Polynomial interpolation is a classical method to approximate<\/jats:p><jats:p>continuous functions by polynomials. To measure the correctness of the<\/jats:p><jats:p>approximation, Lebesgue constants are introduced. For a given node system $X^{(n+1)}=\\{x_1&amp;lt;\\ldots&amp;lt;x_{n+1}\\}\\, (x_j\\in [a,b])$, the Lebesgue function $\\lambda_n(x)$ is the sum of the modulus of the Lagrange basis polynomials built on $X^{(n+1)}$. The Lebesgue constant $\\Lambda_n$ assigned to the function $\\lambda_n(x)$ is its maximum  over $[a,b]$. The Lebesgue constant bounds the interpolation error, i.e., the interpolation polynomial is at most $(1+\\Lambda_n)$ times worse then the best approximation.<\/jats:p><jats:p>The minimum of the $\\Lambda_n$'s for fixed $n$ and interval $[a,b]$ is called the optimal Lebesgue constant $\\Lambda_n^*$.<\/jats:p><jats:p>For specific interpolation node systems such as the equidistant system, numerical results for the Lebesgue constants $\\Lambda_n$ and their asymptotic<\/jats:p><jats:p>behavior are known \\cite{3,7}. However, to give explicit symbolic expression for the minimal Lebesgue constant $\\Lambda_n^*$ is computationally difficult. In this work, motivated by Rack \\cite{5,6},  we are interested for expressing the minimal<\/jats:p><jats:p>Lebesgue constants symbolically on $[-1,1]$ and we are also looking for the<\/jats:p><jats:p>characterization of the those node systems which realize the<\/jats:p><jats:p>minimal Lebesgue constants. We exploited the equioscillation property of the Lebesgue function \\cite{4} and<\/jats:p><jats:p>used quantifier elimination and Groebner Basis as tools \\cite{1,2}. Most of the computation is done in Mathematica \\cite{8}.<\/jats:p>","DOI":"10.29007\/89cm","type":"proceedings-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T17:59:06Z","timestamp":1516730346000},"page":"125-123","source":"Crossref","is-referenced-by-count":0,"title":["Lebesgue Constants and Optimal Node Systems via Symbolic Computations"],"prefix":"10.29007","volume":"15","author":[{"given":"Robert","family":"Vajda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"11545","event":{"name":"SCSS 2013. 5th International Symposium on Symbolic Computation in Software Science"},"container-title":["EPiC Series in Computing"],"original-title":[],"deposited":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T17:59:10Z","timestamp":1516730350000},"score":1,"resource":{"primary":{"URL":"https:\/\/easychair.org\/publications\/paper\/WtHl"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.29007\/89cm","relation":{},"ISSN":["2398-7340"],"issn-type":[{"type":"print","value":"2398-7340"}],"subject":[]}}