Pulications T.J. Dekker, last change February 2010

Ph.D. research (1954-1959)

J. de Groot & T. J. Dekker, Free subgroups of the orthogonal group; Comp. Math. 12, 134-136 (1954).
J. de Groot & T. J. Dekker, Decompositions of a sphere; Proc. Int. Congr. Math. II, 209 (1954).
J. de Groot & T. J. Dekker, Decompositions of a sphere; Fund. Math. 43, 185-194 (1956).
T. J. Dekker, Decompositions of sets and spaces I, II; Indagationes Math. 18, 581-595 (1956).
T. J. Dekker, Decompositions of sets and spaces III; Indagationes Math. 19, 104-107 (1957).
T. J. Dekker, On free products of cyclic rotation groups; Can. J. Math. 11, 67-69 (1959).
T. J. Dekker, On freegroups of motions without fixed points; Indag. Math. 20, 348-353 (1958).
T. J. Dekker, Paradoxical decompositions of sets and spaces; thesis Amsterdam (1958).
T. J. Dekker, On reflections in Euclidean spaces generating free products; Nieuw Archief v. Wiskunde 7, 57-60 (1959).

Numerical sofware edited by the Mathematical Centre, Amsterdam (1959-1963)

T. J. Dekker, Programming for the ARMAC, VI, Matrix complex RAM; Report MR 30 (dutch, 1959).

T. J. Dekker, A set of subroutines for the Electrologica X1, P 101-166: operations on vectors and matrices, numerical algebra (dutch, 1961-1962).
T. J. Dekker, A set of subroutines for the Electrologica X1, P76-86: subroutines for using the Creed 3000 puncher (dutch, 1963).
T. J. Dekker, Assemblages A 1-23: descriptions of some collections of subroutines and some programs and users manuals (dutch, 1961-1963).
T. J. Dekker (editor), Series AP 200-260: ALGOL 60 procedures on numerical algebra and analysis (1962-1965).
T. J. Dekker, Series AP 400-406: ALGOL 60 programs for calculating eigenvalues and eigenvectors and for factor analysis (dutch, 1963).

Numerical analysis and numerical sofware (1968-1997)

T. J. Dekker, Newton-Laguerre iteration; Programmation en Mathématiques Numeriques, C.N.R.S., Paris, 189-200 (1968).
T. J. Dekker, Finding a zero by means of successive linear interpolation; Constructive aspects of the fundamental theorem of algebra, Wiley-Interscience, 37-48 (1969).
T. J. Dekker, ALGOL 60 procedures in numerical algebra, part 1; Mathematical Centre Tracts 22 (1968).
T. J. Dekker & W. Hoffmann, ALGOL 60 procedures in numerical algebra, part 2; Mathematical Centre Tracts 23 (1968).
T. J. Dekker, Calculation of eigenvalues and eigenvectors; Informatie 11, 118-124 (1969).
T. J. Dekker, A floating-point technique for extending the available precision; Num. Math. 18, 224-242 (1971).
T. J. Dekker & J. F. Traub, The shifted QR algorithm for Hermitian matrices; Linear algebra and its applications 4, 137-154 (1971).
T. J. Dekker & J. F. Traub, An analysis of the shifted LR algorithm; Num. Math. 17, 179-188 (1971).
J. C. P. Bus & T. J. Dekker, Two efficient algorithms with guaranteed convergence for finding a zero of a function; ACM TOMS 1, 330-345 (1975).
T. J. Dekker & T. H. P. Reijmer, Zeros of polynomials. Two ALGOL 60 Procedures for calculating all zeros and corresponding error bounds of a polynomial with real coefficients; ACCULIB, Utrecht University (1976).
T. J. Dekker, Elements of numerical linear algebra; Design and implementation of optimization software, edited by H. J. Greenberg; NATO ASI series E: Applied Sciences no 28, Sijthoff & Noordhoff, 103-108 (1978).
T. J. Dekker, Machine requirements for reliable, portable software; Portability of numerical software, edited by W. Cowell; Lecture notes in CS 57, Springer-Verlag, 22-36 (1976).

Pulications T.J. Dekker, continued

T. J. Dekker, Correctness proofs and machine arithmetic; Performance evaluation of numerical software, edited by L. D. Fosdick; North-Holland, 31-43 (1979).
T. J. Dekker, Design of languages for numerical algorithms; Production and assessment of numerical software, edited by M. A. Hennell & L. M. Delves; Acad. Press, 291-305 (1980).
T. J. Dekker, Program correctness and machine arithmetic; Problems and methodologies in mathematical software production, edited by P. C. Messina & A. Murli; Lecture notes in CS no 142, Springer-Verlag, 48-80 (1982).
H. J. J. Te Riele, T. J. Dekker & H. A. Van der Vorst (editors), Algorrithms and Applications on Vector and Parallel Computers: North Holland, Amsterdam (1987).
T. J. Dekker & W. Hoffmann, Numerical improvement of the Gauss-Jordan algorithm; Proceedings ICIAM 87 edited by A.H.P. van der Burgh & R.M.M. Mattheij, Paris-La Vilette, 143-150 (1987).
T. J. Dekker, W. Hoffmann & P.P.M. de Rijk, Algorithms for solving numerical linear algebra problems on supercomputers; Future Generation Computer Systems 4, 255-263 (1988/89).
T. J. Dekker, W. Hoffmann & P.P.M. de Rijk, Portable software in numerical linear algebra for supercomputers; Proceedings of the Symposium on Scientific Software, edited by D.Y. Cai, L.D. Fosdick & H. C. Huang; China University of Science and Technology Press, Beijing, 15-26 (1989).
T. J. Dekker & W. Hoffmann, Rehabilitation of the Gauss-Jordan algorithm; Numerische Mathematik 54, 591-599 (1989).
T. J. Dekker, W. Hoffmann & K. Potma, Parallel algorithms for solving large linear systems; Journal of Computational and applied mathematics 50, 221-232 (1994).
T. J. Dekker, W. Hoffmann & K. Potma, Stability of the Gauss-Huard algorithm with partial pivoting; Computing 58, 225-244 (1997).

Number theory (1994-2010)

T. J. Dekker, Prime numbers in quadratic fields; CWI Quarterly 7, 367-394 (1994).
T. J. Dekker, Priemgetallenpatronen (Patterns of prime numbers); Tilde 7 #2, Studievereniging WEIS, UvA, Amsterdam, 8-11 (dutch, 1995).
T. J. Dekker, Primes in quadratic fields; arXiv:1001.5214v1 [math.NT] (2010) & website http://www.science.uva.nl/~dirk/ (2003, revised 2008-2010).
T. J. Dekker, Priemgetallen en priemidealen in kwadratische lichamen; website http://www.science.uva.nl/~dirk/ (dutch, 2005, herzien 2008-2010).

Syllabi (dutch, 1965-1972)

T. J. Dekker, Cursus Wetenschappelijk Rekenen A, Numerieke wiskunde, I, II, III (Course on Numerical analysis, 3 volumes); Mathematical Centre, Amsterdam (1965-1967).
L. Dekker, T. J. Dekker, P. J. Van der Houwen & M. N. Spijker, Colloquium Stabiliteit van differentieschema's, deel 2; MC Syllabus 2.2, Mathematical Centre, Amsterdam (1968).
T. J. Dekker & C. J. Roothart, Inleiding in de Numerieke wiskunde, Syllabus bij oriënterend colloquium Informatica; Report CR 24/71, Mathematical Centre, Amsterdam (1971).
T. J. Dekker, Numerieke algebra; MC Syllabus 12, Mathematical Centre, Amsterdam (1971).
T. J. Dekker, P. W. Hemker & P. J. Van der Houwen, Colloquium Stijve Differentiaalvergelijkingen (Stiff ODEs) deel 1; MC Syllabus 15.1, Mathematical Centre, Amsterdam (1972).
T. J. Dekker, Syllabus Informatica, deel 1: ALGOL 60 programmering, deel 2: Toepassingen; Instituut voor Toepassingen van de Wiskunde, Universiteit van Amsterdam (1972 en latere edities).

End of Publications T.J. Dekker, last change February 2010