Table Of Content

Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Interval arithmetic to handle uncertainties and to assess numerical quality Nathalie Revol INRIA - Universit´e de Lyon LIP (UMR 5668 CNRS - ENS Lyon - INRIA - UCBL) Journ´ee GAMNI-MAIRCI Pr´ecision et incertitudes, 1er f´evrier 2012 NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Who invented Interval Arithmetic? (cid:73) 1962: Ramon Moore defines IA in his PhD thesis and then a rather exhaustive study of IA in a book in 1966 (cid:73) 1958: Tsunaga, in his MSc thesis in Japanese (cid:73) 1956: Warmus (cid:73) 1951: Dwyer, in the specific case of closed intervals (cid:73) 1931: Rosalind Cecil Young in her PhD thesis in Cambridge (UK) has used some formulas (cid:73) 1927: Bradis, for positive quantities, in Russian (cid:73) 1908: Young, for some bounded functions, in Italian (cid:73) 3rd century BC: Archimedes, to compute an enclosure of π! Cf. http://www.cs.utep.edu/interval-comp/, click on Early papers by Others. NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Who invented Interval Arithmetic? (cid:73) 1962: Ramon Moore defines IA in his PhD thesis and then a rather exhaustive study of IA in a book in 1966 (cid:73) 1958: Tsunaga, in his MSc thesis in Japanese (cid:73) 1956: Warmus (cid:73) 1951: Dwyer, in the specific case of closed intervals (cid:73) 1931: Rosalind Cecil Young in her PhD thesis in Cambridge (UK) has used some formulas (cid:73) 1927: Bradis, for positive quantities, in Russian (cid:73) 1908: Young, for some bounded functions, in Italian (cid:73) 3rd century BC: Archimedes, to compute an enclosure of π! Cf. http://www.cs.utep.edu/interval-comp/, click on Early papers by Others. NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Who invented Interval Arithmetic? (cid:73) 1962: Ramon Moore defines IA in his PhD thesis and then a rather exhaustive study of IA in a book in 1966 (cid:73) 1958: Tsunaga, in his MSc thesis in Japanese (cid:73) 1956: Warmus (cid:73) 1951: Dwyer, in the specific case of closed intervals (cid:73) 1931: Rosalind Cecil Young in her PhD thesis in Cambridge (UK) has used some formulas (cid:73) 1927: Bradis, for positive quantities, in Russian (cid:73) 1908: Young, for some bounded functions, in Italian (cid:73) 3rd century BC: Archimedes, to compute an enclosure of π! Cf. http://www.cs.utep.edu/interval-comp/, click on Early papers by Others. NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Who invented Interval Arithmetic? (cid:73) 1962: Ramon Moore defines IA in his PhD thesis and then a rather exhaustive study of IA in a book in 1966 (cid:73) 1958: Tsunaga, in his MSc thesis in Japanese (cid:73) 1956: Warmus (cid:73) 1951: Dwyer, in the specific case of closed intervals (cid:73) 1931: Rosalind Cecil Young in her PhD thesis in Cambridge (UK) has used some formulas (cid:73) 1927: Bradis, for positive quantities, in Russian (cid:73) 1908: Young, for some bounded functions, in Italian (cid:73) 3rd century BC: Archimedes, to compute an enclosure of π! Cf. http://www.cs.utep.edu/interval-comp/, click on Early papers by Others. NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Who invented Interval Arithmetic? (cid:73) 1962: Ramon Moore defines IA in his PhD thesis and then a rather exhaustive study of IA in a book in 1966 (cid:73) 1958: Tsunaga, in his MSc thesis in Japanese (cid:73) 1956: Warmus (cid:73) 1951: Dwyer, in the specific case of closed intervals (cid:73) 1931: Rosalind Cecil Young in her PhD thesis in Cambridge (UK) has used some formulas (cid:73) 1927: Bradis, for positive quantities, in Russian (cid:73) 1908: Young, for some bounded functions, in Italian (cid:73) 3rd century BC: Archimedes, to compute an enclosure of π! Cf. http://www.cs.utep.edu/interval-comp/, click on Early papers by Others. NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Who invented Interval Arithmetic? (cid:73) 1962: Ramon Moore defines IA in his PhD thesis and then a rather exhaustive study of IA in a book in 1966 (cid:73) 1958: Tsunaga, in his MSc thesis in Japanese (cid:73) 1956: Warmus (cid:73) 1951: Dwyer, in the specific case of closed intervals (cid:73) 1931: Rosalind Cecil Young in her PhD thesis in Cambridge (UK) has used some formulas (cid:73) 1927: Bradis, for positive quantities, in Russian (cid:73) 1908: Young, for some bounded functions, in Italian (cid:73) 3rd century BC: Archimedes, to compute an enclosure of π! Cf. http://www.cs.utep.edu/interval-comp/, click on Early papers by Others. NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Who invented Interval Arithmetic? (cid:73) 1962: Ramon Moore defines IA in his PhD thesis and then a rather exhaustive study of IA in a book in 1966 (cid:73) 1958: Tsunaga, in his MSc thesis in Japanese (cid:73) 1956: Warmus (cid:73) 1951: Dwyer, in the specific case of closed intervals (cid:73) 1931: Rosalind Cecil Young in her PhD thesis in Cambridge (UK) has used some formulas (cid:73) 1927: Bradis, for positive quantities, in Russian (cid:73) 1908: Young, for some bounded functions, in Italian (cid:73) 3rd century BC: Archimedes, to compute an enclosure of π! Cf. http://www.cs.utep.edu/interval-comp/, click on Early papers by Others. NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Who invented Interval Arithmetic? (cid:73) 1962: Ramon Moore defines IA in his PhD thesis and then a rather exhaustive study of IA in a book in 1966 (cid:73) 1958: Tsunaga, in his MSc thesis in Japanese (cid:73) 1956: Warmus (cid:73) 1951: Dwyer, in the specific case of closed intervals (cid:73) 1931: Rosalind Cecil Young in her PhD thesis in Cambridge (UK) has used some formulas (cid:73) 1927: Bradis, for positive quantities, in Russian (cid:73) 1908: Young, for some bounded functions, in Italian (cid:73) 3rd century BC: Archimedes, to compute an enclosure of π! Cf. http://www.cs.utep.edu/interval-comp/, click on Early papers by Others. NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment Introductiontointervalarithmetic Verifiedsolutionsoflinearsystems Variantsofintervalarithmetic Conclusions Historical remarks Childhood until the seventies. Popularization in the 1980, German school (U. Kulisch). IEEE-754 standard for floating-point arithmetic in 1985: directed roundings are standardized and available (?). IEEE-1788 standard for interval arithmetic in 2014? I hope so... NathalieRevol-INRIA-Universit´edeLyon-LIP Intervalarithmetic:uncertaintiesandaccuracy’sassessment

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Précision et incertitudes, 1er février 2012. Nathalie Revol - INRIA - Université de Lyon - LIP. Interval arithmetic: uncertainties and accuracy's assessment
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Précision et incertitudes, 1er février 2012. Nathalie Revol - INRIA - Université de Lyon - LIP. Interval arithmetic: uncertainties and accuracy's assessment

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