On alternative quantization for doubly weighted approximation and integration over unbounded domains

It is known that for a ϱ -weighted L q approximation of single variable functions defi...
Ausführliche Beschreibung

It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals. Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Kritzer, P. [verfasserIn] Pillichshammer, F. [verfasserIn] Plaskota, L. [verfasserIn] Wasilkowski, G.W. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Quantization weighted approximation weighted integration unbounded domains piecewise Taylor approximation

Übergeordnetes Werk:	Enthalten in: Journal of approximation theory - Amsterdam [u.a.] : Elsevier, 1968, 256
Übergeordnetes Werk:	volume:256

DOI / URN:	10.1016/j.jat.2020.105433

Katalog-ID:	ELV004146247

Internformat


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245	1	0	\|a On alternative quantization for doubly weighted approximation and integration over unbounded domains
264		1	\|c 2020
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337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals.
650		4	\|a Quantization
650		4	\|a weighted approximation
650		4	\|a weighted integration
650		4	\|a unbounded domains
650		4	\|a piecewise Taylor approximation
700	1		\|a Pillichshammer, F. \|e verfasserin \|4 aut
700	1		\|a Plaskota, L. \|e verfasserin \|4 aut
700	1		\|a Wasilkowski, G.W. \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Journal of approximation theory \|d Amsterdam [u.a.] : Elsevier, 1968 \|g 256 \|h Online-Ressource \|w (DE-627)266890598 \|w (DE-600)1468964-9 \|w (DE-576)103373136 \|7 nnns
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912			\|a GBV_ILN_63
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912			\|a GBV_ILN_73
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912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2003
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912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
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912			\|a GBV_ILN_4307
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912			\|a GBV_ILN_4322
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912			\|a GBV_ILN_4324
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912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
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936	b	k	\|a 31.40 \|j Analysis: Allgemeines
951			\|a AR
952			\|d 256

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author_variant	p k pk f p fp l p lp g w gw
matchkey_str	kritzerppillichshammerfplaskotalwasilkow:2020----:nlentvqatztofrobyegtdprxmtoadnert
hierarchy_sort_str	2020
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publishDate	2020
allfields	10.1016/j.jat.2020.105433 doi (DE-627)ELV004146247 (ELSEVIER)S0021-9045(20)30069-1 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Kritzer, P. verfasserin aut On alternative quantization for doubly weighted approximation and integration over unbounded domains 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals. Quantization weighted approximation weighted integration unbounded domains piecewise Taylor approximation Pillichshammer, F. verfasserin aut Plaskota, L. verfasserin aut Wasilkowski, G.W. verfasserin aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 256 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:256 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 256
spelling	10.1016/j.jat.2020.105433 doi (DE-627)ELV004146247 (ELSEVIER)S0021-9045(20)30069-1 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Kritzer, P. verfasserin aut On alternative quantization for doubly weighted approximation and integration over unbounded domains 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals. Quantization weighted approximation weighted integration unbounded domains piecewise Taylor approximation Pillichshammer, F. verfasserin aut Plaskota, L. verfasserin aut Wasilkowski, G.W. verfasserin aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 256 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:256 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 256
allfields_unstemmed	10.1016/j.jat.2020.105433 doi (DE-627)ELV004146247 (ELSEVIER)S0021-9045(20)30069-1 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Kritzer, P. verfasserin aut On alternative quantization for doubly weighted approximation and integration over unbounded domains 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals. Quantization weighted approximation weighted integration unbounded domains piecewise Taylor approximation Pillichshammer, F. verfasserin aut Plaskota, L. verfasserin aut Wasilkowski, G.W. verfasserin aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 256 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:256 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 256
allfieldsGer	10.1016/j.jat.2020.105433 doi (DE-627)ELV004146247 (ELSEVIER)S0021-9045(20)30069-1 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Kritzer, P. verfasserin aut On alternative quantization for doubly weighted approximation and integration over unbounded domains 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals. Quantization weighted approximation weighted integration unbounded domains piecewise Taylor approximation Pillichshammer, F. verfasserin aut Plaskota, L. verfasserin aut Wasilkowski, G.W. verfasserin aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 256 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:256 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 256
allfieldsSound	10.1016/j.jat.2020.105433 doi (DE-627)ELV004146247 (ELSEVIER)S0021-9045(20)30069-1 DE-627 ger DE-627 rda eng 510 DE-600 31.40 bkl Kritzer, P. verfasserin aut On alternative quantization for doubly weighted approximation and integration over unbounded domains 2020 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals. Quantization weighted approximation weighted integration unbounded domains piecewise Taylor approximation Pillichshammer, F. verfasserin aut Plaskota, L. verfasserin aut Wasilkowski, G.W. verfasserin aut Enthalten in Journal of approximation theory Amsterdam [u.a.] : Elsevier, 1968 256 Online-Ressource (DE-627)266890598 (DE-600)1468964-9 (DE-576)103373136 nnns volume:256 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT 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_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.40 Analysis: Allgemeines AR 256
language	English
source	Enthalten in Journal of approximation theory 256 volume:256
sourceStr	Enthalten in Journal of approximation theory 256 volume:256
format_phy_str_mv	Article
bklname	Analysis: Allgemeines
institution	findex.gbv.de
topic_facet	Quantization weighted approximation weighted integration unbounded domains piecewise Taylor approximation
dewey-raw	510
isfreeaccess_bool	false
container_title	Journal of approximation theory
authorswithroles_txt_mv	Kritzer, P. @@aut@@ Pillichshammer, F. @@aut@@ Plaskota, L. @@aut@@ Wasilkowski, G.W. @@aut@@
publishDateDaySort_date	2020-01-01T00:00:00Z
hierarchy_top_id	266890598
dewey-sort	3510
id	ELV004146247
language_de	englisch
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author	Kritzer, P.
spellingShingle	Kritzer, P. ddc 510 bkl 31.40 misc Quantization misc weighted approximation misc weighted integration misc unbounded domains misc piecewise Taylor approximation On alternative quantization for doubly weighted approximation and integration over unbounded domains
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topic_title	510 DE-600 31.40 bkl On alternative quantization for doubly weighted approximation and integration over unbounded domains Quantization weighted approximation weighted integration unbounded domains piecewise Taylor approximation
topic	ddc 510 bkl 31.40 misc Quantization misc weighted approximation misc weighted integration misc unbounded domains misc piecewise Taylor approximation
topic_unstemmed	ddc 510 bkl 31.40 misc Quantization misc weighted approximation misc weighted integration misc unbounded domains misc piecewise Taylor approximation
topic_browse	ddc 510 bkl 31.40 misc Quantization misc weighted approximation misc weighted integration misc unbounded domains misc piecewise Taylor approximation
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title	On alternative quantization for doubly weighted approximation and integration over unbounded domains
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title_full	On alternative quantization for doubly weighted approximation and integration over unbounded domains
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author_browse	Kritzer, P. Pillichshammer, F. Plaskota, L. Wasilkowski, G.W.
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title_sort	on alternative quantization for doubly weighted approximation and integration over unbounded domains
title_auth	On alternative quantization for doubly weighted approximation and integration over unbounded domains
abstract	It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals.
abstractGer	It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals.
abstract_unstemmed	It is known that for a ϱ -weighted L q approximation of single variable functions defined on a finite or infinite interval, whose r th derivatives are in a ψ -weighted L p space, the minimal error of approximations that use n samples of f is proportional to ‖ ω 1 ∕ α ‖ L 1 α ‖ f ( r ) ψ ‖ L p n − r + ( 1 ∕ p − 1 ∕ q ) + , where ω = ϱ ∕ ψ and α = r − 1 ∕ p + 1 ∕ q , provided that ‖ ω 1 ∕ α ‖ L 1 < + ∞ . Moreover, the optimal sample points are determined by quantiles of ω 1 ∕ α . In this paper, we show how the error of the best approximation changes when the sample points are determined by a quantizer κ other than ω . Our results can be applied in situations when an alternative quantizer has to be used because ω is not known exactly or is too complicated to handle computationally. The results for q = 1 are also applicable to ϱ -weighted integration over finite and infinite intervals.
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title_short	On alternative quantization for doubly weighted approximation and integration over unbounded domains
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author2	Pillichshammer, F. Plaskota, L. Wasilkowski, G.W.
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up_date	2024-07-06T22:00:20.796Z
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On alternative quantization for doubly weighted approximation and integration over unbounded domains

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