Back to Publications and preprints
Marco Vianello:
complete list of mathematical publications
published or to appear
2018

Subperiodic
Trigonometric Hyperinterpolation,
"Contemporary Computational Mathematics  a celebration of
the 80th birthday
of Ian Sloan"
(invited paper), J. Dick, F.Y.
Kuo, H. Wozniakowski Eds., Springer, 2018 (with G. Da Fies and A.
Sommariva).

An elementary approach to polynomial optimization on polynomial
meshes,
J. Math. Fund. Sci. 50 (2018).
2017

A note on total degree polynomial optimization by Chebyshev grids,
Optim. Lett., published online 01 July 2017 (with F. Piazzon).
 Numerical
quadrature on the intersection of planar disks,
FILOMAT 31:13 (2017), 41054115 (with A. Sommariva).

Subperiodic
trigonometric subsampling: a numerical approach,
Appl. Anal. Discrete Math. 11 (2017), 470483 (with A. Sommariva).
 CaratheodoryTchakaloff Least Squares,
2017 International Conference on Sampling Theory and Applications
(SampTA), IEEE Xplore Digital Library, DOI: 10.1109/SAMPTA.2017.8024337
(with F. Piazzon and A. Sommariva).

Numerical
hyperinterpolation over nonstandard planar regions,
Math. Comput. Simulation 141 (2017), 110120
(with A.
Sommariva).

On the use of compressed polyhedral quadrature formulas in embedded
interface
methods,
SIAM J. Sci Comput. 39 (2017), B571B587
(with Y. Sudhakar, A. Sommariva and W.A. Wall).

Optimal polynomial meshes and CaratheodoryTchakaloff submeshes on
the sphere, Dolomites Res. Notes Approx. DRNA 10 (2017),
1824 (with P. Leopardi and A. Sommariva).
 CaratheodoryTchakaloff Subsampling,
Dolomites Res. Notes Approx. DRNA 10 (2017), 514
(with F. Piazzon and A. Sommariva).

Polynomial approximation on Lissajous curves in the dcube,
Appl. Numer. Math. 116 (2017), 4756 (with L. Bos
and S. De Marchi).
 Polynomial approximation and quadrature on geographic
rectangles, Appl. Math. Comput. 297 (2017), 159179
(with M. Gentile and A. Sommariva).
 Trivariate
polynomial approximation on Lissajous curves, IMA J. Numer. Anal.,
37 (2017), 519541 (with L. Bos
and
S. De Marchi).
2016
 Jacobi norming meshes,
Math. Inequal. Appl. 19 (2016), 10891095 (with F. Piazzon).
 Compressed
sampling
inequalities by Tchakaloff's theorem,
Math. Inequal. Appl. 19 (2016), 395400.
2015
 Compression of multivariate discrete measures and
applications,
Numer. Funct. Anal. Optim. 36 (2015), 11981223
(with A. Sommariva).
 Polynomial fitting and interpolation on circular sections,
Appl. Math. Comput. 258 (2015), 410424
(with A. Sommariva).
 Polynomial
Meshes: Computation and Approximation, Proceeedings of CMMSE 2015,
414425, ISBN 9788461722303, ISSN 23120177 (with S. De Marchi, F.
Piazzon and A. Sommariva).
2014
 Suboptimal polynomial meshes
on planar Lipschitz domains,
Numer. Funct. Anal. Optim. 35 (2014), 14671475
(with F. Piazzon).
 Product Gaussian quadrature on circular
lunes,
Numer. Math. Theory Methods Appl. 7 (2014), 251264 (with G. Da
Fies).
 Constructing optimal polynomial meshes on planar starlike
domains,
Dolomites Res. Notes Approx. DRNA 7 (2014), 2225 (with F. Piazzon).
 Norming meshes by Bernsteinlike
inequalities, Math. Inequal. Appl. 17 (2014), 929936.
 Multivariate Christoffel functions and hyperinterpolation,
Dolomites Res. Notes Approx. DRNA 7
(2014), 2633 (with S. De Marchi, A.
Sommariva).
2013
 On the Lebesgue constant of subperiodic trigonometric
interpolation,
J. Approx. Theory 167 (2013), 5964 (with G. Da Fies).
 Algebraic cubature by linear blending of
elliptical arcs,
Appl. Numer. Math. 74 (2013), 4961 (with G. Da Fies and
A. Sommariva).
 Small perturbations of polynomial meshes,
Appl. Anal. 92 (2013), 10631073 (with F. Piazzon).
 Polynomial approximation on pyramids, cones
and solids of
rotation,
Dolomites Res. Notes Approx. DRNA 6 (2013), 2026 (with
S. De Marchi).
2012

On the generation of symmetric
Lebesguelike points in the triangle,
J. Comput. Appl. Math. 236 (2012), 49254932
(with F. Rapetti, A. Sommariva).
 Subperiodic trigonometric interpolation and quadrature,
Appl. Math. Comput. 218 (2012), 1063010638 (with L. Bos).
 Trigonometric Gaussian quadrature on subintervals of
the period, Electron. Trans. Numer. Anal. 39 (2012), 102112
(with G. Da Fies).
 Algebraic cubature on planar lenses and bubbles,
Dolomites Res. Notes Approx. DRNA 5 (2012), 712 (with G. Da Fies).
 Computing Fekete and Lebesgue points: simplex, square,
disk, J. Comput. Appl. Math. 236 (2012), 24772486
(with M. Briani, A.
Sommariva).
 Low cardinality admissible meshes on quadrangles,
triangles and disks, Math. Inequal. Appl. 15 (2012), 229235
(with L. Bos).
 The "phase function" method to solve secondorder
asymptotically polynomial differential equations, Numer. Math.
121 (2012), 565586 (with
R. Spigler).
2011

Geometric Weakly Admissible Meshes, Discrete Least Squares
Approximations and Approximate Fekete Points, Math. Comp. 80 (2011),
16011621
(with L. Bos, J.P. Calvi, N. Levenberg, A.
Sommariva).

On Multivariate Newton Interpolation at Discrete Leja
Points,
Dolomites Res. Notes Approx. DRNA 4 (2011), 1520
(with L. Bos, S. De Marchi, A. Sommariva).

Polynomial interpolation and cubature over polygons,
J. Comput. Appl. Math. 235 (2011), 52325239
(with M. Gentile, A. Sommariva).

An algebraic cubature formula on curvilinear polygons, Appl. Math.
Comput. 217 (2011), 1000310015
(with G. Santin, A. Sommariva).
 Padua2DM: fast interpolation and cubature at the Padua
points in
Matlab/Octave,
Numer. Algorithms 56 (2011), 4560 (with M. Caliari, S. De
Marchi, A.
Sommariva).
 Weakly Admissible Meshes and Discrete Extremal Sets,
Numer. Math. Theory Methods Appl. 4 (2011), 112 (with L. Bos, S. De
Marchi, A. Sommariva).
2010

Computing multivariate Fekete and Leja points by numerical linear
algebra, SIAM J. Numer. Anal. 48 (2010), 19841999 (with L. Bos, S.
De Marchi, A. Sommariva).

Analytic transformations of admissible meshes, East J. Approx.
16 (2010), 313322 (with F. Piazzon).
 Leastsquares polynomial approximation on weakly
admissible
meshes: disk and triangle,
J. Comput. Appl. Math. 235 (2010), 660668 (with L. Bos, A.
Sommariva).

On simple approximations to simple curves,
Dolomites Res. Notes Approx. DRNA 3 (2010), 16
(with L. Bos).

Approximate Fekete points for weighted polynomial interpolation,
Electron. Trans. Numer. Anal. 37 (2010), 122 (with A. Sommariva).
2009
 GaussGreen cubature and moment computation over arbitrary
geometries, J. Comput. Appl. Math. 231 (2009), 886896 (with
A. Sommariva).
 A numerical code for fast interpolation and cubature at the
Padua points, Proceedings of the 9th CMMSE (2009), Vol. I, 218228
(with M. Caliari, S. De Marchi, A. Sommariva).
 A massively parallel
exponential integrator for advectiondiffusion models, J. Comput.
Appl. Math. 231 (2009), 8291 (with L. Bergamaschi, M.
Caliari, A. Martinez).
 Computing approximate Fekete points by QR factorizations of
Vandermonde matrices,
Comput. Math. Appl. 57 (2009), 13241336 (with A.
Sommariva).
 New cubature formulae and hyperinterpolation in three
variables,
BIT Numerical Mathematics 49 (2009), 5573 (with S. De
Marchi, Y.
Xu).
2008
 Algorithm 886: Padua2D: Lagrange Interpolation at Padua
Points on Bivariate
Domains, ACM Trans. Math. Software 353 (2008) (with M. Caliari, S.
De Marchi).
 Nontensorial ClenshawCurtis cubature, Numer.
Algorithms 49 (2008), 409427 (with A. Sommariva, R.
Zanovello).
 Hyperinterpolation in the cube, Comput. Math. Appl.
55 (2008), 24902497 (with M. Caliari, S. De
Marchi).
 Bivariate Lagrange interpolation at the Padua points:
computational aspects, J. Comput. Appl. Math. 221 (2008), 284292
(with M. Caliari, S. De Marchi).
 Meshless cubature over the disk by ThinPlate Splines,
J. Comput. Appl. Math. 221 (2008) 430436
(with A. Punzi and A. Sommariva).
 Asymptotic approximations for secondorder linear difference
equations in Banach algebras, II, J. Math. Anal. Appl. 340
(2008), 433450 (with T. Solda`, R. Spigler).
 Asymptotic approximations for secondorder linear difference
equations in Banach algebras, I, J. Math. Anal. Appl. 337 (2008),
11581170 (with T. Solda`, R. Spigler).
2007
 Bivariate Lagrange interpolation at the Padua points:
the ideal theory approach, Numer. Math. 108 (2007), 4357 (with L.
Bos, S. De Marchi, Y. Xu).
 Product Gauss cubature over polygons based on Green's
integration formula,
BIT Numerical Mathematics 47 (2007), 441453
(with A. Sommariva).
 The LEM exponential integrator for
advectiondiffusionreaction
equations, J. Comput. Appl. Math. 210 (2007), 5663 (with L.
Bergamaschi, M. Caliari).
 Hyperinterpolation on the square, J. Comput. Appl.
Math. 210 (2007), 7883 (with M. Caliari, S. De
Marchi).
 LiouvilleGreen asymptotic approximation for a class of
matrix
differential equations and semidiscretized partial differential
equations, J. Math. Anal. Appl. 325 (2007), 6989 (with R.
Spigler).
2006
 Bivariate Lagrange interpolation at the Padua points: the
generating curve approach, J. Approx. Theory 143 (2006), 1525
(with L. Bos, M. Caliari, S. De Marchi, Y. Xu).
 Meshless cubature by Green's formula, Appl. Math.
Comput. 183 (2006), 10981107 (with A. Sommariva).
 Hyper2d: a numerical code for hyperinterpolation on
rectangles, Appl. Math. Comput. 183 (2006), 11381147
(with M. Caliari, S. De Marchi, R. Montagna).
 Bivariate interpolation at Xu points: results, extensions
and
applications, Electron. Trans. Numer. Anal. 25 (2006), 116
(with L. Bos, M. Caliari, S. De Marchi).
 On the Lebesgue constant for the Xu interpolation
formula,
J. Approx. Theory 141 (2006), 134141 (with L. Bos, S. De Marchi).
 Comparing Krylov and Leja approximations of large scale
matrix
exponentials,
Springer LNCS vol. 3994, part IV, 2006 (Proc. of ICCS 2006, Reading, UK),
685692
(with L. Bergamaschi, M. Caliari, A. Martinez).
 A numerical study of the Xu polynomial interpolation formula
in two variables, Computing 76 (2006), 311324 (with
L. Bos, M. Caliari, S. De Marchi).
 Numerical cubature
on scattered data by radial basis functions,
Computing 76 (2006), 295310 (with A. Sommariva).
 LiouvilleGreen asymptotics for almostdiagonal secondorder
matrix differential equations, Asymptotic Analysis 48 (2006), 267294
(with R. Spigler).
2005
 Bivariate polynomial
interpolation on the square at new nodal sets, Appl. Math. Comput. 165
(2005), 261274 (with M. Caliari, S. De Marchi).
 Adaptive bivariate
Chebyshev approximation, Numer. Algorithms 38 (2005),
7994 (with A. Sommariva, R. Zanovello).
 A parallel exponential integrator for largescale
discretizations of advectiondiffusion models,
Springer LNCS vol. 3666, 2005 (Proc. of Euro PVM MPI 2005,
Sorrento,
Italy), 483492 (with L. Bergamaschi, M. Caliari, A.
Martinez).
2004
 The ReLPM exponential integrator for FE discretizations of
advectiondiffusion equations,
Springer LNCS vol. 3039, part IV, 2004 (Proc. of ICCS 2004,
Krakow,
Poland), 434442 (with L. Bergamaschi, M. Caliari).
 Adaptive bivariate Chebyshev approximation and efficient
evaluation of integral operators,
Appl. Numer. Anal. Comput. Math. 1 (2004), 115121
(with A. Mardegan, A. Sommariva, R. Zanovello).
 Interpolating discrete
advectiondiffusion propagators at Leja sequences, J. Comput. Appl.
Math.
172 (2004), 7999 (with L. Bergamaschi, M.
Caliari).
2003
 Fast evaluation of discrete
integral
transforms by Chebyshev and Leja polynomial approximation,
Constructive
theory of functions, 347353, DARBA, Sofia, 2003 (with
S. De Marchi).
 Efficient approximation of the exponential operator for
discrete 2D
advectiondiffusion problems,
Numer. Linear Algebra Appl. 10 (2003), 271289 (with
L. Bergamaschi, M. Caliari).
2001
 Approximating the
approximant: a
numerical code for polynomial compression of discrete integral
operators,
In memory of W. Gross. Numer. Algorithms 28 (2001),
101116 (with S. De Marchi).
 Fast summation of
power series with coefficients analytic at infinity, Numer. Algorithms
27
(2001), 7787 (with A. Sommariva, R. Zanovello).
 Positive multiplication
preserves
dissipativity in commutative C*algebras, J. Inequal. Appl. 6
(2001), 247251 (with A. Sommariva).
2000
 Chebyshevlike compression of linear and
nonlinear
discretized integral operators, Neural Parallel Sci. Comput. 8 (2000),
327353.
 Computing positive
fixedpoints of
decreasing Hammerstein operators by relaxed iterations, J. Integral
Equations Appl. 12 (2000), 95112 (with A.
Sommariva).
 Relaxed
Picardlike
methods
for nonlinear integral equations arising in transport theory, Applied
and
industrial mathematics, Venice2, 1998, 273285, Kluwer Acad. Publ.,
Dordrecht, 2000 (with E. Facchinello, A. Sommariva).
 Efficient computation of the
exponential operator for large, sparse, symmetric matrices, Numer.
Linear
Algebra Appl. 7 (2000), 2745 (with L.
Bergamaschi).
 A new summation method
for power series with rational coefficients, Math. Comp. 69 (2000),
749756 (with S. Dassie`, R. Zanovello).
 A variant of the complex
LiouvilleGreen
approximation theorem, Arch. Math. (Brno) 36 (2000),
213218 (with R. Spigler).
 Existence of positive continuous solutions of
perturbed
Hammerstein equations, Appl. Anal. 74 (2000),
429438.
 Constructive approximation
for a
class
of perturbed Hammerstein integral equations, Nonlinear Anal. 41
(2000), Ser. A: Theory Methods, 177185 (with A.
Sommariva).
1999
 LiouvilleGreenOlver approximations for complex difference
equations, J. Approx. Theory 96 (1999), 301322
(with F. Locatelli, R. Spigler).
 Constructive analysis of
purely
integral Boltzmann models, J. Integral Equations Appl. 11 (1999),
393404 (with A. Sommariva).
 On the complex differential
equation
Y"+G(z)Y=0 in Banach algebras, Stud. Appl. Math. 102 (1999),
291308 (with R. Spigler).
1998
 Asymptotic summation
of power series, Numer. Math. 80 (1998), 6173
(with S. Dassie`, R. Zanovello).
 Approximating fixedpoints of
decreasing operators in spaces of continuous functions, Numer. Funct.
Anal. Optim. 19 (1998), 635646 (with A.
Sommariva).
1997
 Peano's kernel theorem for
vectorvalued functions: a weak version in normed spaces, Numer.
Funct.
Anal. Optim. 18 (1997), 6574 (with S. De
Marchi).
 A survey on the
LiouvilleGreen (WKB)
approximation for linear difference equations of the second order,
Advances in difference equations (Veszprem, 1995), 567577, Gordon and
Breach, Amsterdam, 1997 (with R. Spigler).
1996
 Peano's kernel theorem for
vectorvalued functions and some applications, Numer. Funct. Anal.
Optim.
17 (1996), 5764 (with S. De Marchi).
 Asymptotic representation for
the
BlumenthalNevai orthogonal polynomials in the essential spectrum,
Methods Appl. Anal. 3 (1996), 457475 (with R.
Spigler).
 WKBtype approximations for
secondorder differential equations in C*algebras, Proc. Amer.
Math. Soc. 124 (1996), 17631771 (with R.
Spigler).
1995
 Convergence analysis of the
semiimplicit Euler method for abstract evolution equations,
Numer. Funct. Anal. Optim. 16 (1995), 785803
(with R. Spigler).
 On some connections between
wellposedness
and general properties of numerical methods, Z. Angew. Math. Mech. 75
(1995), 237241 (with R. Zanovello).
 On regularity at t=0 for semilinear ADEs and
its
numerical applications, Semigroup Forum 50 (1995),
97104.
1994
 Splitting functions
and numerical analysis of WRtype methods for evolutionary and stationary
problems, Mathematics of Computation 19431993: a halfcentury of
computational mathematics (Vancouver, BC, 1993), 281285, Proc. Sympos.
Appl. Math., 48, Amer. Math. Soc., Providence, RI, 1994
(with S. De Marchi, R. Zanovello).
 Semiimplicit discretization
of
abstract
evolution equations, Equadiff 8 (Bratislava, 1993), Tatra Mt. Math.
Publ.
4 (1994), 207212 (with R. Spigler).
 Discrete and continuous
LiouvilleGreenOlver approximations: a unified treatment via
VolterraStieltjes integral equations, SIAM J. Math. Anal. 25 (1994),
720732 (with R. Spigler).
1993
 Cesaro's theorems for complex
sequences,
J. Math. Anal. Appl. 180 (1993), 317324 (with
R. Spigler).
 Abstract versions of
L'Hopital's
rule
for holomorphic functions in the framework of complex Bmodules, J.
Math. Anal. Appl. 180 (1993), 1728 (with R.
Spigler).
 Extending L'Hopital's theorem
to Bmodules, J. Math. Anal. Appl. 179 (1993), 638645
(with R. Spigler).
 Finite moments perturbations of
y"=0 in Banach algebras, Proc. Amer. Math. Soc. 119 (1993),
97103 (with R. Spigler).
 A generalization of l'Hopital's rule via
absolute
continuity and Banach modules, Real Anal. Exchange 18 (1992/93),
557567.
1992
 Extensions and numerical applications of the LiouvilleGreen
approximation, Ph.D. Thesis,
Italian NorthEastern Doctoral School in Computational Mathematics
(Universities of Bologna, Padova, Trieste and Udine), 184
 On the superlinear
convergence of the
secant method, Amer. Math. Monthly 99 (1992), 758761
(with R. Zanovello).
 LiouvilleGreen approximations
for
a class of linear oscillatory difference equations of the second
order,
Asymptotic methods in analysis and combinatorics, J. Comput. Appl. Math.
41 (1992), 105116 (with
R. Spigler).
 Improved estimates for the
derivatives
of the Osymbols in view of numerical applications, J. Math. Anal.
Appl.
164 (1992), 480488 (with
R. Spigler).
 WKBJtype approximation for
finite
moments perturbations of the differential equation y"=0 and the
analogous difference equation, J. Math. Anal. Appl. 169 (1992),
437452 (with
R. Spigler).
1991
 Global existence and uniqueness
for the
Kummer transformation problem subject to nonCauchy data, Differential
Integral Equations 4 (1991), 9911003 (with
R. Spigler).
1990
 A numerical method for
evaluating zeros
of solutions of secondorder linear differential equations, Math.
Comp.
55 (1990), 591612 (with R. Spigler).
 Approximating zeros of solutions of
secondorder linear ODEs by "phase function" methods, Asymptotic and
computational analysis (Winnipeg, MB, 1989), 707722, Lecture Notes in
Pure and Appl. Math., 124, Dekker, New York, 1990 (with
R. Spigler).