Veronika Pillwein

Research Area

Special Functions, High order finite elements

Office

Schloss Hagenberg
A-4232 Hagenberg im Mühlkreis

Room: -2.11-2

Postal Adress

Research Institute for Symbolic Computation
Johannes Kepler University
Altenberger Straße 69
A-4040 Linz, Austria

Publications

2016

A hypergeometric inequality

A. Dixit, V.H. Moll, V. Pillwein

Annals of Combinatorics 20(1), pp. 65-72. 2016. 0218-0006. [pdf]
[bib]
@article{RISC4965,
author = {A. Dixit and V.H. Moll and V. Pillwein},
title = {{A hypergeometric inequality}},
language = {english},
journal = {Annals of Combinatorics},
volume = {20},
number = {1},
pages = {65--72},
isbn_issn = {0218-0006},
year = {2016},
refereed = {yes},
length = {8}
}

2015

An extension of Turan's inequality for ultraspherical polynomials

G. Nikolov, V. Pillwein

Mathematical Inequalities & Applications 18(1), pp. 321-335. 2015. [pdf]
[bib]
@article{RISC4953,
author = {G. Nikolov and V. Pillwein},
title = {{An extension of Turan's inequality for ultraspherical polynomials}},
language = {english},
journal = {Mathematical Inequalities & Applications},
volume = {18},
number = {1},
pages = {321--335},
isbn_issn = {?},
year = {2015},
refereed = {yes},
length = {15}
}

Proof of a conjecture of M. Patrick concerning Jacobi polynomials

A. Alexandrov, H. Dietert, G. Nikolov, V. Pillwein

Journal of Mathematical Analysis and Applications 428(2), pp. 750-761. 2015.
[bib]
@article{RISC5140,
author = {A. Alexandrov and H. Dietert and G. Nikolov and V. Pillwein},
title = {{Proof of a conjecture of M. Patrick concerning Jacobi polynomials }},
language = {english},
journal = {Journal of Mathematical Analysis and Applications},
volume = {428},
number = {2},
pages = {750--761},
isbn_issn = {?},
year = {2015},
refereed = {yes},
length = {12}
}

Symbolic Computation and Finite Element Methods.

V. Pillwein

In: CASC 2015, V.P. Gerdt, W. Koepf, W.M. Seiler, and E.V. Vorozhtsov (ed.), LNCS 9301, pp. 374-388. 2015. Springer-Verlag Berlin Heidelberg, 0302-9743. [pdf]
[bib]
@inproceedings{RISC5182,
author = {V. Pillwein},
title = {{Symbolic Computation and Finite Element Methods.}},
booktitle = {{CASC 2015}},
language = {english},
series = {LNCS},
volume = {9301},
pages = {374--388},
publisher = {Springer-Verlag Berlin Heidelberg},
isbn_issn = {0302-9743},
year = {2015},
editor = {V.P. Gerdt and W. Koepf and W.M. Seiler and and E.V. Vorozhtsov},
refereed = {no},
length = {15}
}

An efficient procedure deciding positivity for a class of holonomic sequences

V. Pillwein, M. Schussler

ACM Communications in Computer Algebra 49(3), pp. 90-93. 2015. Extended abstract of the poster presentation at ISSAC 2015. [pdf]
[bib]
@article{RISC5617,
author = {V. Pillwein and M. Schussler},
title = {{An efficient procedure deciding positivity for a class of holonomic sequences}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {49},
number = {3},
pages = {90--93},
isbn_issn = { },
year = {2015},
note = {Extended abstract of the poster presentation at ISSAC 2015},
refereed = {yes},
length = {4}
}

2014

A local Fourier convergence analysis of a multigrid method using symbolic computation

V. Pillwein, S. Takacs

Journal of Symbolic Computation 63, pp. 1-20. 2014. ISSN:0747-7171 . [pdf]
[bib]
@article{RISC4907,
author = {V. Pillwein and S. Takacs},
title = {{A local Fourier convergence analysis of a multigrid method using symbolic computation}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {63},
pages = {1--20},
isbn_issn = {ISSN:0747-7171 },
year = {2014},
refereed = {yes},
length = {20}
}

A note on uniform approximation of functions having a double pole

I. Moale, V. Pillwein

LMS J. Comput. Math. 17(1), pp. 233-244. 2014. [pdf]
[bib]
@article{RISC4908,
author = {I. Moale and V. Pillwein},
title = {{A note on uniform approximation of functions having a double pole}},
language = {english},
journal = {LMS J. Comput. Math.},
volume = {17},
number = {1},
pages = {233--244},
isbn_issn = {?},
year = {2014},
refereed = {yes},
length = {12}
}

2013

Harmonic interpolation based on Radon projections along the sides of regular polygons

Irina Georgieva, Clemens Hofreither, Christoph Koutschan, Veronika Pillwein, Thotsaporn Thanatipanonda

Central European Journal of Mathematics 11(4), pp. 609-620. 2013. ISSN 1895-1074. [pdf]
[bib]
@article{RISC4655,
author = {Irina Georgieva and Clemens Hofreither and Christoph Koutschan and Veronika Pillwein and Thotsaporn Thanatipanonda},
title = {{Harmonic interpolation based on Radon projections along the sides of regular polygons}},
language = {english},
abstract = {Given information about a harmonic function in two variables, consisting of a finitenumber of values of its Radon projections, i.e., integrals along some chords of the unitcircle, we study the problem of interpolating these data by a harmonic polynomial.With the help of symbolic summation techniques we show that this interpolationproblem has a unique solution in the case when the chords form a regular polygon.Numerical experiments for this and more general cases are presented.},
journal = {Central European Journal of Mathematics},
volume = {11},
number = {4},
pages = {609--620},
isbn_issn = {ISSN 1895-1074},
year = {2013},
refereed = {yes},
length = {12}
}

Sparsity optimized high order finite element functions for H(curl) on tetrahedra

S. Beuchler and V. Pillwein and S. Zaglmayr

Advances in Applied Mathematics 50, pp. 749-769. 2013. [url] [pdf]
[bib]
@article{RISC4663,
author = {S. Beuchler and V. Pillwein and S. Zaglmayr},
title = {{Sparsity optimized high order finite element functions for H(curl) on tetrahedra}},
language = {english},
journal = {Advances in Applied Mathematics},
volume = {50},
pages = {749--769},
isbn_issn = {?},
year = {2013},
refereed = {yes},
length = {20},
url = {http://dx.doi.org/10.1016/j.aam.2012.11.004}
}

Termination Conditions for Positivity Proving Procedures

V. Pillwein

In: Proceedings of ISSAC'13, M. Kauers (ed.), pp. 315-322. 2013. isbn 978-1-4503-2059-7/13/06. [pdf]
[bib]
@inproceedings{RISC4714,
author = {V. Pillwein},
title = {{Termination Conditions for Positivity Proving Procedures}},
booktitle = {{Proceedings of ISSAC'13}},
language = {english},
abstract = { Proving positivity of a sequence given by a linear recurrence with polynomial coefficients (P-finite recurrence) is a non-trivial task for both humans and computers. Algorithms dealing with this task are rare or non-existent. One method that was introduced in the last decade by Gerhold and Kauers succeeds on many examples, but termination of this procedure has been proven so far only up to order three for special cases. Here we present an analysis that extends the previously known termination results on recurrences of order three, and also provides termination conditions for recurrences of higher order.},
pages = {315--322},
isbn_issn = {isbn 978-1-4503-2059-7/13/06},
year = {2013},
editor = {M. Kauers},
refereed = {yes},
length = {7}
}

2012

Fast summation techniques for sparse shape functions in tetrahedral hp-FEM

S. Beuchler, V. Pillwein and S. Zaglmayr

In: Domain Decomposition Methods in Science and Engineering XX, , pp. 537-544. 2012. to appear. [pdf]
[bib]
@inproceedings{RISC3283,
author = {S. Beuchler and V. Pillwein and S. Zaglmayr},
title = {{Fast summation techniques for sparse shape functions in tetrahedral hp-FEM}},
booktitle = {{Domain Decomposition Methods in Science and Engineering XX}},
language = {english},
pages = {537--544},
isbn_issn = {?},
year = {2012},
note = {to appear},
editor = {?},
refereed = {yes},
length = {8}
}

Sparsity optimized high order finite element functions for H(div) on simplices

S. Beuchler, V. Pillwein and S. Zaglmayr

Numerische Mathematik 122(2), pp. 197-225. 2012. [pdf]
[bib]
@article{RISC4524,
author = {S. Beuchler and V. Pillwein and S. Zaglmayr},
title = {{Sparsity optimized high order finite element functions for H(div) on simplices}},
language = {english},
journal = {Numerische Mathematik},
volume = {122},
number = {2},
pages = {197--225},
isbn_issn = {?},
year = {2012},
refereed = {yes},
length = {29}
}

Closed form solutions of linear difference equations in terms of symmetric products

Y. Cha, V. Pillwein

ACM Communications in Computer Algebra 46(3-4), pp. 80-81. Sep 2012. 0.
[bib]
@article{RISC5616,
author = {Y. Cha and V. Pillwein},
title = {{Closed form solutions of linear difference equations in terms of symmetric products}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {46},
number = {3-4},
pages = {80--81},
isbn_issn = {0},
year = {2012},
month = {Sep},
refereed = {yes},
length = {2}
}

2011

Sparsity optimized high order finite element functions on simplices

S. Beuchler, V. Pillwein, J. Schoeberl and S. Zaglmayr

In: Numerical and Symbolic Scientific Computing: Progress and Prospects, Ulrich Langer and Peter Paule (ed.), pp. 21-44. 2011. Springer, Wien, [pdf]
[bib]
@incollection{RISC4253,
author = {S. Beuchler and V. Pillwein and J. Schoeberl and S. Zaglmayr },
title = {{Sparsity optimized high order finite element functions on simplices}},
booktitle = {{Numerical and Symbolic Scientific Computing: Progress and Prospects}},
language = {english},
pages = {21--44},
publisher = {Springer},
address = {Wien},
isbn_issn = {?},
year = {2011},
editor = {Ulrich Langer and Peter Paule},
refereed = {yes},
length = {24}
}

Automatic Improvements of Wallis' Inequality

P. Paule, V. Pillwein

In: SYNASC 2010, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, T. Ida and others (ed.), pp. 12-16. 2011. IEEE Computer Society, 0. [pdf]
[bib]
@inproceedings{RISC4297,
author = {P. Paule and V. Pillwein},
title = {{Automatic Improvements of Wallis' Inequality}},
booktitle = {{SYNASC 2010, 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing}},
language = {english},
pages = {12--16},
publisher = {IEEE Computer Society},
isbn_issn = {0},
year = {2011},
editor = {T.~Ida and others},
refereed = {no},
length = {5}
}

Dominance in the Family of Sugeno-Weber t-norms

Manuel Kauers, Veronika Pillwein, Susanne Saminger-Platz

Fuzzy Sets and Systems 181(1), pp. 74-87. October 2011. ISSN 0165-0114. [ps] [pdf]
[bib]
@article{RISC4328,
author = {Manuel Kauers and Veronika Pillwein and Susanne Saminger-Platz},
title = {{Dominance in the Family of Sugeno-Weber t-norms}},
language = {english},
abstract = {The dominance relationship between two members of the family of Sugeno Weber t-norms is proven by using a quantifer elimination algorithm. Further it is shown that dominance is a transitive, and therefore also an order relation, on this family of t-norms.},
journal = {Fuzzy Sets and Systems},
volume = {181},
number = {1},
pages = {74--87},
isbn_issn = {ISSN 0165-0114},
year = {2011},
month = {October},
refereed = {yes},
length = {14}
}

On the Average Complexity for the Verification of Compatible Sequences

C. Koukouvinos, V. Pillwein, D.E. Simos, Z. Zafeirakopoulos

Information Processing Letters 111(17), pp. 825-830. 2011. [pdf]
[bib]
@article{RISC4352,
author = {C. Koukouvinos and V. Pillwein and D.E. Simos and Z. Zafeirakopoulos},
title = {{On the Average Complexity for the Verification of Compatible Sequences }},
language = {english},
journal = {Information Processing Letters },
volume = {111},
number = {17},
pages = {825--830},
isbn_issn = {?},
year = {2011},
refereed = {yes},
length = {6}
}

Smoothing analysis of an all-at-once multigrid approach for optimal control problems using symbolic computation

V. Pillwein, S. Takacs

In: Numerical and Symbolic Scientific Computing: Progress and Prospects, U. Langer, P. Paule (ed.), pp. 175-192. 2011. Springer Wien, [pdf]
[bib]
@incollection{RISC4520,
author = {V. Pillwein and S. Takacs},
title = {{Smoothing analysis of an all-at-once multigrid approach for optimal control problems using symbolic computation}},
booktitle = {{Numerical and Symbolic Scientific Computing: Progress and Prospects}},
language = {english},
pages = {175--192},
publisher = {Springer Wien},
isbn_issn = {?},
year = {2011},
editor = {U. Langer and P. Paule},
refereed = {yes},
length = {18}
}

2010

When can we detect that a P-finite sequence is positive?

Manuel Kauers, Veronika Pillwein

In: Proceedings of ISSAC'10, Stephen Watt (ed.), pp. 195-202. 2010. 978-1-4503-0150-3. [pdf] [ps]
[bib]
@inproceedings{RISC4022,
author = {Manuel Kauers and Veronika Pillwein},
title = {{When can we detect that a P-finite sequence is positive?}},
booktitle = {{Proceedings of ISSAC'10}},
language = {english},
abstract = {We consider two algorithms which can be used for proving positivity ofsequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed on a greatmany examples, there is no guarantee for them to terminate, and theydo in fact not terminate for every input.For some restricted classes of P-finite recurrence equations of order up to three we provide a priori criteria that assert the termination of the algorithms.},
pages = {195--202},
isbn_issn = {978-1-4503-0150-3},
year = {2010},
editor = {Stephen Watt},
refereed = {yes},
length = {7}
}

2009

Equilibrated Residual Error Estimates are $p$-Robust

D. Braess, V. Pillwein, J. Schöberl

Comput. Methods Appl. Mech. Engrg. 198, pp. 1189-1197. 2009. [ps] [pdf]
[bib]
@article{RISC3414,
author = {D. Braess and V. Pillwein and J. Schöberl},
title = {{Equilibrated Residual Error Estimates are $p$-Robust}},
language = {english},
abstract = { Equilibrated residual error estimators applied to high order finite elements are analyzed. The estimators provide always a true upper bound for the energy error. We prove that also the efficiency estimate is robust with respect to the polynomial degrees. The result is complete for tensor product elements. In the case of simplicial elements, the theorem is based on a conjecture, for which numerical evidence is provided.},
journal = {Comput. Methods Appl. Mech. Engrg.},
volume = {198},
pages = {1189--1197},
isbn_issn = {?},
year = {2009},
refereed = {yes},
length = {9}
}

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