Neuere Veröffentlichungen
Buchveröffentlichung
Herausgegebene Bücher
- W. Gautschi, G. H. Golub, G. Opfer (Hrsg.): Applications and Computation of Orthogonal Polynomials,
Birkhäuser, Basel, Boston, Berlin,1999, 268 S., ISNM 131.
Conference at the Mathematical Research Institute Oberwolfach, Germany, March 22-28, 1998.
Dedicated to the Memory of Günther Hämmerlin (1928 - 1997).
Originalarbeiten
- Newton's approach to general algebraic equations over Clifford
algebras,
p. 267 - 276 of S. Bernstein (ed.):Topics in Clifford
Anylysis,
Special volume in honor of Wolfgang Sprößig,
Birkhäuser, 2019, 509 p.
jointly with Drahoslava Janovská.
-
The relation between the companion matrix and the companion
polynomial in $R^4$ algebras,
jointly with Drahoslava Janovská.
published online July 24, 2018 by Adv. Appl. Clifford Algebras.
https://doi.org/10.1007s00006-018-0892-5.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2018-04, Februar 2018, 12 p.
-
Niven's algorithm applied to the roots of the companion polynomial over $R^4$ algebras.
published online: 13 June 2017, Adv. Appl. Clifford Algebras 27 (2017), 2659-2675.
DOI 10.1007/s00006-017-0786-y.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2017-15, 14 p.
-
The number of zeros of unilateral polynomials over coquaternions and related algebras.
jointly with Drahoslava Janovská.
Electronic Transactions on Numerical Analysis (ETNA).
46 (2017), pp. 55-70.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2016-37, December 2016, 16 p.
-
Polynomial interpolation in nondivision algebras.
Electronic Transactions on Numerical Analysis (ETNA).
44 (2015), pp. 660-670.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2015-39, November 2015, 11 p.
-
Matrices over nondivision algebras without eigenvalues,
jointly with Drahoslava Janovská.
Adv. Appl. Clifford Algebras, 26 (2016), pp. 591-612.
http://link.springer.com/article/10.1007/s00006-015-0615-0
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2015-34, October 2015, 18 p.
- On a Toeplitz structure of the characteristic polynomials,
jointly with Drahoslava Janovská.
Proceedings of the $4^{th}$ Scientific Colloquium,
Institute of Chemical Technology, Prague, 2014, pp. 119-131.
-
The Jacobi matrix for functions in noncommutative algebras,
jointly with Reiner Lauterbach.
Advances in Applied Clifford Algebras (AACA), 24 (2014), pp. 1059-1073.
Erratum: Advances in Clifford Algebras (AACA), 24 (2014), p. 1075.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2014-11, May 2014, 12 p.
-
Zeros and singular points for one-sided, coquaternionic polynomials with an extension
to other $\R^4$ algebras,
jointly with Drahoslava Janovská.
Electronic Transactions on Numerical Analysis (ETNA) 41(2014), pp. 133-158.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2014-06, April 2014, 24 p.
-
The algebraic Riccati equation for quaternions,
dedicated to Ivo Marek on the occasion of his 80th birthday,
jointly with Drahoslava Janovská.
Advances in Applied Clifford Algebras, 23 (2013), 907-918.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2013-04, May 2013, 10 p.
-
Linear equations and the Kronecker product in coquaternions,
dedicated to Lothar Reichel on the occasion of his 60th birthday,
jointly with Drahoslava Janovská.
Mitteilungen der Mathematischen Gesellschaft Hamburg, (33) 2013, 181-196.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2013-05, May 2013, 13 p.
- An analytic approach to the Collatz 3n + 1 problem for negative start values,
jointly with Lothar Berg.
Computational Methods and Function Theory (CMFT), 13 (2013), 225-236.
-
An analytic approach to the Collatz 3n + 1 problem for negative start values
with an appendix of tables,
jointly with Lothar Berg.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2012-11, December 2012, 40 p.
-
An analytic approach to the Collatz 3n + 1 problem,
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2011-09, May 2011, 32 p.
-
The Nonexistence of Pseudoquaternions in $\C\power{2\times2}$,
jointly with Drahoslava Janovská.
Advances in Applied Clifford Algebras, 21 (2011), 531-540,
published online: December 24, 2010.
Hamburger Beiträge zur Angewandten Mathematik, Preprint 2010-11, Oktober 2010, 8 p.
-
The classification and the computation of the zeros of quaternionic,
two-sided polynomials,
jointly with Drahoslava Janovská.
Numer. Math., 115 (2010), 81-100, published online: November 18, 2009.
-
A note on the computation of all zeros of simple quaternionic polynomials,
jointly with Drahoslava Janovská.
SIAM J. Numer. Anal. 48 (2010), 244-256, published online: April 2, 2010.
-
Polynomials and Vandermonde Matrices over the Field of Quaternions,
ETNA 36(2009), 9-16.
- Linear equations in quaternionic variables,
gemeinsam mit Drahoslava Janovská.
Mitt. Math. Ges. Hamburg, 27 (2008), 223-234.
-
On Disk-Like Sets and Square Coverings in the Plane -
a Geometric Problem,
Dedicated to Richard S. Varga on the occasion of his 80th birthday.
Result. Math. 53 (2009), 349-359, Birkhäuser, Basel.
-
Decompositions of Quaternions and their Matrix Equivalents,
gemeinsam mit Drahoslava Janovská.
Dedicated to the Memory of Gene Golub.
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
2008-02, March 2008, 9 p.
in V. Olshevsky and E. Tyrtyshnikov (eds.): Matrix Methods: Theory, Algorithms and Applications,
World Scientific, New Jersey, 2010, pp. 20-30.
Proceedings of
2nd INTERNATIONAL CONFERENCE ON MATRIX METHODS AND OPERATOR
EQUATIONS, July 23-27, 2007, Moscow, Russia.
-
On one linear equation in one quaternionic unknown,
gemeinsam mit Drahoslava Janovská,
Dedicated to Bernd Fischer on the occasion of his 50th birthday.
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
2007-14, September 2007, 34 S.
Submitted to Linear Algebra Appl. (but rejected).
-
Computing Quaternionic Roots by Newton's Method,
gemeinsam mit Drahoslava Janovská,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 194, December 2006, 29 S.
ETNA 26(2007), 82-102.
-
Linear equations in quaternions,
gemeinsam mit Drahoslava Janovská,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 193, Mai 2006, 9 S.
Numerical Mathematics and Advanced Applications, Proceedings
of ENUMATH 2005,
A. B. de Castro, D. G\'omez, P. Quintela,
and P. Salgado (eds.),
Springer, Berlin, Heidelberg, New
York, 2006, 945-953, ISBN 3-540-34287-7.
-
Shift Generated Haar Spaces on Track Fields,
dedicated to the memory of Walter Hengartner.
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 191, March 2006, 12 S.
Abstract in English and Armenian.
Journal of Contemporary Mathematical Analysis, 40, 6, 2005, 41-53.
The editor, A. Sahakian, has shortened the abstract and deleted the Armenian
version of the abstract without consent of the author.
Proceedings of a conference on Harmonic Analysis and Approximation, III
in Tsakhadzor, Armenia, September 21-26, 2005. Academy of Science, Erivan.
-
On the Number 50,
dedicated to Marie Luise and Reiner Lauterbach
on the occasion of their 50th birthday.
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 188, October 2005, 32 S.
Mitt. Math. Ges. 24(2005), 151-174.
-
Fast Givens transformation for quaternion valued matrices
applied to Hessenberg reductions,
gemeinsam mit Drahoslava Janovská,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 184, February 2005, 35 S.
ETNA 20(2005), 1-26.
-
The conjugate gradient algorithm applied to quaternion-valued matrices,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 179, March 2004, 28 S.
ZAMM 85(2005)9, 660-672.
-
Shift generated Haar spaces on unbounded, closed domains in the complex plane,
Dedicated to the memory of Dieter Gaier,
gemeinsam mit Maude Giasson und Walter Hengartner,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 175, August 2003, 14 S.
Computational Methods and Function Theory, 3 (2003), 151 - 164.
-
Shift generated Haar spaces on compact domains in the complex plane
,
gemeinsam mit Walter Hengartner,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 174, July 2003, 18 S.
Constr. Approx. 22(2005), 113 - 132.
-
Givens' Transformation Applied to Quaternion Valued Vectors
,
gemeinsam mit Drahoslava Janovská,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 171, February 2003, 12 S.
BIT Numerical Mathematics, 43 (2003), 991 - 1002.
-
Complex Haar Spaces Generated by Shifts Applied to a Single Function
,
with Walter Hengartner,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 167, November 2001, 14 S.
has appeared in: C. K. Chui, L. L. Schumaker, J. Stöckler (eds.),
Approximation Theory X, Abstract and Classical Analysis, pp. 223-238 (2002).
Vanderbilt University Press, Nashville, TN.
ISBN 0-8265-1415-4.
- Hyperbolic Householder and Givens Transformations,
gemeinsam mit Drahoslava Janovská,
Preprint, Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 136, March 1998, 19 S.
A note on hyperbolic transformations,
Numer. Linear Algebra Appl., 8 (2001), 127-146.
The following MATLAB-Programs are referred to in the text:
Hypgiv.m,
Hyphsd.m,
Qrhg.m,
Vechg.m,
Vechh.m,
Zerogiv.m,
Zerohh.m.
- Complex version of Catalan's problem,
gemeinsam mit Wolfgang Ripken,
Mitt. Math. Ges. Hamburg, 17 (1998), 101-112.
-
On the Construction of Optimal Monotone Cubic Spline
Interpolation,
gemeinsam mit Sigrid Fredenhagen und Hans Joachim Oberle,
J. Approx. Theory 96 (1999), 182-201.
-
Non-negative splines, in particular of degree five,
gemeinsam mit Hans Joachim Oberle,
Numer. Math. 79 (1998), 427-450.
- Splines with prescribed modified moments,
gemeinsam mit Hans Joachim Oberle, in: Curves and surfaces in geometric
design,
P.-J. Laurent, A. Le M'ehaut'e, L. L. Schumaker (Eds.), 343-352, 1994.
- On the number of integer dilation matrices used in wavelet theory,
in: Proceedings of the Cornelius Lanczos international centenary conference,
J. D. Brown, M. T. Chu, D. C. Ellison, R. J. Plemmons (Eds.),
SIAM, Philadelphia, 1994, 426-428.
- Faber versus minimal polynomials on annular sectors,
gemeinsam mit Jan Modersitzki, Computational Methods and
Function Theory 1994,
R. M. Ali, St. Ruscheweyh, E. B. Saff (Eds.),
World Scientific, Singapore, 1995, 243-265.
- Display of zeros of orthogonal polynomials on annular sectors,
Hamburger Beiträge zur Angewandten Mathematik,
Reihe A, 87, Oktober 1994.
gerhard.opfer@uni-hamburg.de,
31. Dezember 2019