%$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters

Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Du, Jiarui [verfasserIn] Zhu, Yuanpeng Han, Xuli

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Smoothing Exponential splines Sixth order differential operator C continuity

Anmerkung:	© The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Calcolo - Milano : Springer Italia, 1964, 59(2022), 4 vom: Nov.
Übergeordnetes Werk:	volume:59 ; year:2022 ; number:4 ; month:11

Links:	Volltext

DOI / URN:	10.1007/s10092-022-00487-0

Katalog-ID:	SPR04861064X

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520			\|a Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed.
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700	1		\|a Zhu, Yuanpeng \|0 (orcid)0000-0001-8682-6089 \|4 aut
700	1		\|a Han, Xuli \|4 aut
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912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
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912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
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912			\|a GBV_ILN_602
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912			\|a GBV_ILN_2006
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allfields	10.1007/s10092-022-00487-0 doi (DE-627)SPR04861064X (SPR)s10092-022-00487-0-e DE-627 ger DE-627 rakwb eng Du, Jiarui verfasserin aut %$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed. Smoothing (dpeaa)DE-He213 Exponential splines (dpeaa)DE-He213 Sixth order differential operator (dpeaa)DE-He213 C (dpeaa)DE-He213 continuity (dpeaa)DE-He213 Zhu, Yuanpeng (orcid)0000-0001-8682-6089 aut Han, Xuli aut Enthalten in Calcolo Milano : Springer Italia, 1964 59(2022), 4 vom: Nov. (DE-627)271597038 (DE-600)1480691-5 1126-5434 nnns volume:59 year:2022 number:4 month:11 https://dx.doi.org/10.1007/s10092-022-00487-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 59 2022 4 11
spelling	10.1007/s10092-022-00487-0 doi (DE-627)SPR04861064X (SPR)s10092-022-00487-0-e DE-627 ger DE-627 rakwb eng Du, Jiarui verfasserin aut %$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed. Smoothing (dpeaa)DE-He213 Exponential splines (dpeaa)DE-He213 Sixth order differential operator (dpeaa)DE-He213 C (dpeaa)DE-He213 continuity (dpeaa)DE-He213 Zhu, Yuanpeng (orcid)0000-0001-8682-6089 aut Han, Xuli aut Enthalten in Calcolo Milano : Springer Italia, 1964 59(2022), 4 vom: Nov. (DE-627)271597038 (DE-600)1480691-5 1126-5434 nnns volume:59 year:2022 number:4 month:11 https://dx.doi.org/10.1007/s10092-022-00487-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 59 2022 4 11
allfields_unstemmed	10.1007/s10092-022-00487-0 doi (DE-627)SPR04861064X (SPR)s10092-022-00487-0-e DE-627 ger DE-627 rakwb eng Du, Jiarui verfasserin aut %$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed. Smoothing (dpeaa)DE-He213 Exponential splines (dpeaa)DE-He213 Sixth order differential operator (dpeaa)DE-He213 C (dpeaa)DE-He213 continuity (dpeaa)DE-He213 Zhu, Yuanpeng (orcid)0000-0001-8682-6089 aut Han, Xuli aut Enthalten in Calcolo Milano : Springer Italia, 1964 59(2022), 4 vom: Nov. (DE-627)271597038 (DE-600)1480691-5 1126-5434 nnns volume:59 year:2022 number:4 month:11 https://dx.doi.org/10.1007/s10092-022-00487-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 59 2022 4 11
allfieldsGer	10.1007/s10092-022-00487-0 doi (DE-627)SPR04861064X (SPR)s10092-022-00487-0-e DE-627 ger DE-627 rakwb eng Du, Jiarui verfasserin aut %$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed. Smoothing (dpeaa)DE-He213 Exponential splines (dpeaa)DE-He213 Sixth order differential operator (dpeaa)DE-He213 C (dpeaa)DE-He213 continuity (dpeaa)DE-He213 Zhu, Yuanpeng (orcid)0000-0001-8682-6089 aut Han, Xuli aut Enthalten in Calcolo Milano : Springer Italia, 1964 59(2022), 4 vom: Nov. (DE-627)271597038 (DE-600)1480691-5 1126-5434 nnns volume:59 year:2022 number:4 month:11 https://dx.doi.org/10.1007/s10092-022-00487-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 59 2022 4 11
allfieldsSound	10.1007/s10092-022-00487-0 doi (DE-627)SPR04861064X (SPR)s10092-022-00487-0-e DE-627 ger DE-627 rakwb eng Du, Jiarui verfasserin aut %$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed. Smoothing (dpeaa)DE-He213 Exponential splines (dpeaa)DE-He213 Sixth order differential operator (dpeaa)DE-He213 C (dpeaa)DE-He213 continuity (dpeaa)DE-He213 Zhu, Yuanpeng (orcid)0000-0001-8682-6089 aut Han, Xuli aut Enthalten in Calcolo Milano : Springer Italia, 1964 59(2022), 4 vom: Nov. (DE-627)271597038 (DE-600)1480691-5 1126-5434 nnns volume:59 year:2022 number:4 month:11 https://dx.doi.org/10.1007/s10092-022-00487-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 59 2022 4 11
language	English
source	Enthalten in Calcolo 59(2022), 4 vom: Nov. volume:59 year:2022 number:4 month:11
sourceStr	Enthalten in Calcolo 59(2022), 4 vom: Nov. volume:59 year:2022 number:4 month:11
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topic_facet	Smoothing Exponential splines Sixth order differential operator C continuity
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container_title	Calcolo
authorswithroles_txt_mv	Du, Jiarui @@aut@@ Zhu, Yuanpeng @@aut@@ Han, Xuli @@aut@@
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author	Du, Jiarui
spellingShingle	Du, Jiarui misc Smoothing misc Exponential splines misc Sixth order differential operator misc C misc continuity %$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters
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topic_title	%$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters Smoothing (dpeaa)DE-He213 Exponential splines (dpeaa)DE-He213 Sixth order differential operator (dpeaa)DE-He213 C (dpeaa)DE-He213 continuity (dpeaa)DE-He213
topic	misc Smoothing misc Exponential splines misc Sixth order differential operator misc C misc continuity
topic_unstemmed	misc Smoothing misc Exponential splines misc Sixth order differential operator misc C misc continuity
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title	%$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters
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title_full	%$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters
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author_browse	Du, Jiarui Zhu, Yuanpeng Han, Xuli
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title_sort	%$c^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters
title_auth	%$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters
abstract	Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed. © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed. © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have %$C^4%$ continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed. © The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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container_issue	4
title_short	%$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters
url	https://dx.doi.org/10.1007/s10092-022-00487-0
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author2	Zhu, Yuanpeng Han, Xuli
author2Str	Zhu, Yuanpeng Han, Xuli
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doi_str	10.1007/s10092-022-00487-0
up_date	2024-07-03T20:20:02.710Z
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%$C^4%$ interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters

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