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The remaining five chapters concern specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting. The present text version differs from the original in several respects. The book is now typeset (in plain TeX), the Fortran programs now make use of Fortran 77 features. The figures have been redrawn with the aid of Matlab, various errors have been corrected, and many more formal statements have been provided with proofs. Further, all formal statements and equations have been numbered by the same numbering system, to make it easier to find any particular item. A major change has occured in Chapters IX-XI where the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. This has brought in knot insertion as a powerful tool for providing simple proofs concerning the shape-preserving properties of the B-spline series.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50275165896977,"sku":"CIN0387903569G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ WELL_READ \/ SBYB","offer_id":50571329569041,"sku":"CIN0387903569A","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50960814276881,"sku":"CIN0387903569VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51853127352593,"sku":"GOR003409211","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387903569.jpg?v=1786110251"},{"product_id":"box-splines-book-carl-de-boor-9780387941011","title":"Box Splines","description":"Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and other smooth functions of one and several arguments. 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This revised edition has been typeset, and all figures have been redrawn. In a major change, the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. Almost all formal statements are now provided with proofs, and many minor changes have been made throughout, including the correction of errors.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51002002145553,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51002004799761,"sku":"NIN9780387953663","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ LIKE_NEW \/ INTERNAL","offer_id":51462140723473,"sku":"GOR014289185","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51524245520657,"sku":"GOR008564511","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52139957944593,"sku":"NLS9780387953663","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387953663.jpg?v=1751006753"},{"product_id":"fasti-censorii-book-carl-de-boor-9781020439186","title":"Fasti Censorii ......","description":null,"brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51114324984081,"sku":"NIN9781020439186","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1020439181.jpg?v=1786183631"},{"product_id":"nicephori-archiepiscopi-constantinopolitani-opuscula-historica-book-carl-de-boor-9781021079497","title":"Nicephori Archiepiscopi Constantinopolitani Opuscula Historica","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51163912896785,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51163914961169,"sku":"NIN9781021079497","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1021079499.jpg?v=1786183972"},{"product_id":"fasti-censorii-book-carl-de-boor-9781022389731","title":"Fasti Censorii ......","description":null,"brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51271724630289,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51271726530833,"sku":"NIN9781022389731","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1022389734.jpg?v=1751174321"},{"product_id":"splinefunktionen-book-carl-de-boor-9783764325145","title":"Splinefunktionen","description":"Der Begriff der Splinefunktionen wurde von I. J. Schoenberg 1946 eingefUhrt. \"Spline\" ist der Name eines Zeichengerates, welches auf mechanischem Weg Interpolatio- aufgaben lost. Dieses Gerat besteht aus einer flexiblen, oft mehrere Meter langen Latte, die auf dem Zeichenbrett aufliegt und dort an bestimmten Stellen durch Gewichte festgehalten wird. Die Form, die die Latte annimmt, hangt von den Elastizitatseigenschaften der Latte abo -, \" , , , , , , \\ , \\ \\ I , , , ,\" -\"', , , , , J::\u0026gt;----\" , I I , I I I , , , , , , , , , , , \" ) Fig. 1: Latteninterpo1ation Po1ynominterpo1ation _ - - - - - - - --0 Wir konnen natUrlich versuchen, ein mathematisches Modell fUr dieses mechanische Zeichengerat zu machen, d. h. die Gestalt solcher Kurven mathematisch zu erfassen. - 2 - Die Theorie der Balkenbiegung verlangt, dass die mittlere 2 K quadratische KrUmmung, (\"strain energy\", Spannungs- J energie) minimiert wird.\nLasst sich die Kurve als Graph einer Funktion f auf dem Intervall [a,b] schreiben, so erhalt man mit dem bekannten Ausdruck fUr die Krlimmung K [f\" (t) P --------------dt ~ min (1) t [1 +f' (t)2J5\/2 a Statt dieses schwierige Extremalproblem zu losen, begnUgt man sich damit, (2) zu minimieren. Die Extremalfunktion fUr das Funktional (2) ist stUckweise ein kubisches Polynom; die Polyn- stUcke gehen an den Bruchstellen so glatt ineinander Uber, dass die Funktion zweimal stetig differenzierbar ist.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52144113123601,"sku":"NLS9783764325145","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783764325145.jpg?v=1786033481"},{"product_id":"box-splines-book-carl-de-boor-9781441928344","title":"Box Splines","description":"Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and other smooth functions of one and several arguments. Since they are locally polynomial, they are easy to evaluate. 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