A Note on Lagrange Interpolation of |<i>x</i>| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases
Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the error of the Lagrange polynomial interpolants of the functi...
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/15/2558 |
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| author | Elías Berriochoa Alicia Cachafeiro Héctor García-Rábade José Manuel García-Amor |
| author_facet | Elías Berriochoa Alicia Cachafeiro Héctor García-Rábade José Manuel García-Amor |
| author_sort | Elías Berriochoa |
| collection | DOAJ |
| description | Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the error of the Lagrange polynomial interpolants of the function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></semantics></math></inline-formula> on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>, using Chebyshev and Chebyshev–Lobatto nodal systems with an even number of points. Moreover, with respect to the odd cases, relevant changes in the shape and the extrema of the error are given. |
| first_indexed | 2024-03-09T05:14:23Z |
| format | Article |
| id | doaj.art-d3bfda6671af41eaaf48c58cf747ef26 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T05:14:23Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d3bfda6671af41eaaf48c58cf747ef262023-12-03T12:47:06ZengMDPI AGMathematics2227-73902022-07-011015255810.3390/math10152558A Note on Lagrange Interpolation of |<i>x</i>| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even CasesElías Berriochoa0Alicia Cachafeiro1Héctor García-Rábade2José Manuel García-Amor3Departamento de Matemática Aplicada I, Universidad de Vigo, 36310 Vigo, SpainDepartamento de Matemática Aplicada I, Universidad de Vigo, 36310 Vigo, SpainDepartamento de Matemática Aplicada II, Universidad de Vigo, 32004 Ourense, SpainXunta de Galicia, Instituto E. S. Valle Inclán, 36001 Pontevedra, SpainThroughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the error of the Lagrange polynomial interpolants of the function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></semantics></math></inline-formula> on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>, using Chebyshev and Chebyshev–Lobatto nodal systems with an even number of points. Moreover, with respect to the odd cases, relevant changes in the shape and the extrema of the error are given.https://www.mdpi.com/2227-7390/10/15/2558Lagrange interpolationChebyshev nodal systemsChebyshev–Lobatto nodal systemsabsolute value approximationrate of convergenceGibbs–Wilbraham phenomena |
| spellingShingle | Elías Berriochoa Alicia Cachafeiro Héctor García-Rábade José Manuel García-Amor A Note on Lagrange Interpolation of |<i>x</i>| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases Mathematics Lagrange interpolation Chebyshev nodal systems Chebyshev–Lobatto nodal systems absolute value approximation rate of convergence Gibbs–Wilbraham phenomena |
| title | A Note on Lagrange Interpolation of |<i>x</i>| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases |
| title_full | A Note on Lagrange Interpolation of |<i>x</i>| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases |
| title_fullStr | A Note on Lagrange Interpolation of |<i>x</i>| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases |
| title_full_unstemmed | A Note on Lagrange Interpolation of |<i>x</i>| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases |
| title_short | A Note on Lagrange Interpolation of |<i>x</i>| on the Chebyshev and Chebyshev–Lobatto Nodal Systems: The Even Cases |
| title_sort | note on lagrange interpolation of i x i on the chebyshev and chebyshev lobatto nodal systems the even cases |
| topic | Lagrange interpolation Chebyshev nodal systems Chebyshev–Lobatto nodal systems absolute value approximation rate of convergence Gibbs–Wilbraham phenomena |
| url | https://www.mdpi.com/2227-7390/10/15/2558 |
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