Brass, Helmut; Petras, Knut Quadrature theory. The theory of numerical integration on a compact interval. (English) Zbl 1231.65059 Mathematical Surveys and Monographs 178. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5361-0/hbk). vii, 363 p. (2011). Reviewer: Jesus Illán González (Vigo) MSC: 65D32 65D30 41A55 41A80 65-02 41A63 PDFBibTeX XMLCite \textit{H. Brass} and \textit{K. Petras}, Quadrature theory. The theory of numerical integration on a compact interval. Providence, RI: American Mathematical Society (AMS) (2011; Zbl 1231.65059)
Brass, Helmut; Petras, Knut Bounds for norms of Peano kernels. (English) Zbl 1111.41022 East J. Approx. 9, No. 2, 195-207 (2003). MSC: 41A50 41A55 PDFBibTeX XMLCite \textit{H. Brass} and \textit{K. Petras}, East J. Approx. 9, No. 2, 195--207 (2003; Zbl 1111.41022)
Petras, K. Bounds for the third Peano constants of Gaussian quadrature formulae. (English) Zbl 0928.65035 Acta Math. Hung. 83, No. 3, 241-250 (1999). Reviewer: Mariana Gaspar (Iasi) MSC: 65D32 41A55 41A80 PDFBibTeX XMLCite \textit{K. Petras}, Acta Math. Hung. 83, No. 3, 241--250 (1999; Zbl 0928.65035) Full Text: DOI
Petras, Knut Quadrature error estimates involving moduli of continuity of derivatives. (English) Zbl 0904.41020 Proceedings of the 3rd international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, September 23–28, 1996. Vols. I and II. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 52, 707-722 (1998). MSC: 41A55 41A80 PDFBibTeX XMLCite \textit{K. Petras}, in: Proceedings of the 3rd international conference on functional analysis and approximation theory, Acquafredda di Maratea (Potenza), Italy, September 23--28, 1996. Vols. I and II. Palermo: Circolo Matemàtico di Palermo. 707--722 (1998; Zbl 0904.41020)
Petras, Knut On the universality of the Gaussian quadrature formula. (English) Zbl 0865.41032 East J. Approx. 2, No. 4, 427-438 (1996). Reviewer: A.Bultheel (Leuven) MSC: 41A55 PDFBibTeX XMLCite \textit{K. Petras}, East J. Approx. 2, No. 4, 427--438 (1996; Zbl 0865.41032)
Petras, K. On the integration of functions having singularities. (English) Zbl 0850.65029 Z. Angew. Math. Mech. 75, Suppl. 2, S655-S656 (1995). MSC: 65D32 41A55 41A80 PDFBibTeX XMLCite \textit{K. Petras}, Z. Angew. Math. Mech. 75, S655--S656 (1995; Zbl 0850.65029)
Petras, Knut Duality and lower bounds for relative projection constants. (English) Zbl 0873.41009 J. Approximation Theory 81, No. 1, 104-119 (1995). Reviewer: K.Petras (Braunschweig) MSC: 41A10 41A55 PDFBibTeX XMLCite \textit{K. Petras}, J. Approx. Theory 81, No. 1, 104--119 (1995; Zbl 0873.41009) Full Text: DOI Link
Petras, Knut High order error constants of Clenshaw-Curtis product rules. (English) Zbl 0799.65022 Analysis 14, No. 1, 1-18 (1994). Reviewer: S.Filippi (Gießen) MSC: 65D32 41A55 41A80 PDFBibTeX XMLCite \textit{K. Petras}, Analysis 14, No. 1, 1--18 (1994; Zbl 0799.65022) Full Text: DOI
Petras, Knut One sided \(L_ 1\)-approximation and bounds for Peano kernels. (English) Zbl 0749.41027 Numerical integration. Recent developments, software and applications, Proc. NATO Adv. Res. Workshop, Bergen/Norw. 1991, NATO ASI Ser., Ser. C 357, 165-174 (1992). Reviewer: R.S.Dahiya (Ames) MSC: 41A55 PDFBibTeX XMLCite \textit{K. Petras}, in: Numerical integration. Recent developments, software and applications. Proceedings of the NATO advanced research workshop, Bergen, Norway, June 17-22, 1991. . 165--174 (1992; Zbl 0749.41027)
Petras, Knut Error estimates for Filon quadrature formulae. (English) Zbl 0697.41018 BIT 30, No. 3, 529-541 (1990). MSC: 41A55 41A25 PDFBibTeX XMLCite \textit{K. Petras}, BIT 30, No. 3, 529--541 (1990; Zbl 0697.41018) Full Text: DOI