Back to Home Page

Marco Vianello: scientific and didactic curriculum


Short CV

Research results

Author of
see on the personal web page http://www.math.unipd.it/~marcov the following:

relevant topics

most relevant achievements (with selected papers)


selected codes

Research collaboration and coordination experience

Conference organization and editorial experience

Research evaluation experience

Selected presentations at international conferences

Complete list of mathematical publications

    published or to appear

    2018

  1. Discrete norming inequalities on sections of sphere, ball and torus, J. Inequal. Spec. Funct., to appear (with A. Sommariva).
  2. Subperiodic Dubiner distance, norming meshes and trigonometric polynomial optimization, Optim. Lett., published online 15 March 2018.
  3. Nearly optimal nested sensors location for polynomial regression on complex geometries, Sampl. Theory Signal Image Process. 17 (2018), 95--101 (with A. Sommariva).
  4. Global polynomial optimization by norming sets on sphere and torus, Dolomites Res. Notes Approx. DRNA 11 (2018), 10--14.
  5. Stability inequalities for Lebesgue constants via Markov-like inequalities, Dolomites Res. Notes Approx. DRNA 11 (2018), 1--9 (with F. Piazzon).
  6. Subperiodic Trigonometric Hyperinterpolation, in: "Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan" (invited paper), J. Dick, F.Y. Kuo, H. Wozniakowski Eds., Springer, 2018, pp. 283--304 (with G. Da Fies and A. Sommariva).
  7. An elementary approach to polynomial optimization on polynomial meshes, J. Math. Fund. Sci. 50 (2018), 84--91.
  8. A note on total degree polynomial optimization by Chebyshev grids, Optim. Lett. 12 (2018), 63--71 (with F. Piazzon).

    2017

  9. Numerical quadrature on the intersection of planar disks, FILOMAT 31:13 (2017), 4105--4115 (with A. Sommariva).
  10. Subperiodic trigonometric subsampling: a numerical approach, Appl. Anal. Discrete Math. 11 (2017), 470--483 (with A. Sommariva).
  11. Caratheodory-Tchakaloff 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).
  12. Numerical hyperinterpolation over nonstandard planar regions, Math. Comput. Simulation 141 (2017), 110--120 (with A. Sommariva).
  13. On the use of compressed polyhedral quadrature formulas in embedded interface methods, SIAM J. Sci Comput. 39 (2017), B571-B587 (with Y. Sudhakar, A. Sommariva and W.A. Wall).
  14. Optimal polynomial meshes and Caratheodory-Tchakaloff submeshes on the sphere, Dolomites Res. Notes Approx. DRNA 10 (2017), 18--24 (with P. Leopardi and A. Sommariva).
  15. Caratheodory-Tchakaloff Subsampling, Dolomites Res. Notes Approx. DRNA 10 (2017), 5--14 (with F. Piazzon and A. Sommariva).
  16. Polynomial approximation on Lissajous curves in the d-cube, Appl. Numer. Math. 116 (2017), 47--56 (with L. Bos and S. De Marchi).
  17. Polynomial approximation and quadrature on geographic rectangles, Appl. Math. Comput. 297 (2017), 159--179 (with M. Gentile and A. Sommariva).
  18. Trivariate polynomial approximation on Lissajous curves, IMA J. Numer. Anal. 37 (2017), 519--541 (with L. Bos and S. De Marchi).

    2016

  19. Jacobi norming meshes, Math. Inequal. Appl. 19 (2016), 1089--1095 (with F. Piazzon).
  20. Compressed sampling inequalities by Tchakaloff's theorem, Math. Inequal. Appl. 19 (2016), 395--400.

    2015

  21. Compression of multivariate discrete measures and applications, Numer. Funct. Anal. Optim. 36 (2015), 1198--1223 (with A. Sommariva).
  22. Polynomial fitting and interpolation on circular sections, Appl. Math. Comput. 258 (2015), 410--424 (with A. Sommariva).
  23. Polynomial Meshes: Computation and Approximation, Proceeedings of CMMSE 2015, 414--425, ISBN 978-84-617-2230-3, ISSN 2312-0177 (with S. De Marchi, F. Piazzon and A. Sommariva).

    2014

  24. Sub-optimal polynomial meshes on planar Lipschitz domains, Numer. Funct. Anal. Optim. 35 (2014), 1467--1475 (with F. Piazzon).
  25. Product Gaussian quadrature on circular lunes, Numer. Math. Theory Methods Appl. 7 (2014), 251--264 (with G. Da Fies).
  26. Constructing optimal polynomial meshes on planar starlike domains, Dolomites Res. Notes Approx. DRNA 7 (2014), 22--25 (with F. Piazzon).
  27. Norming meshes by Bernstein-like inequalities, Math. Inequal. Appl. 17 (2014), 929--936.
  28. Multivariate Christoffel functions and hyperinterpolation, Dolomites Res. Notes Approx. DRNA 7 (2014), 26--33 (with S. De Marchi, A. Sommariva).

    2013

  29. On the Lebesgue constant of subperiodic trigonometric interpolation, J. Approx. Theory 167 (2013), 59--64 (with G. Da Fies).
  30. Algebraic cubature by linear blending of elliptical arcs, Appl. Numer. Math. 74 (2013), 49--61 (with G. Da Fies and A. Sommariva).
  31. Small perturbations of polynomial meshes, Appl. Anal. 92 (2013), 1063--1073 (with F. Piazzon).
  32. Polynomial approximation on pyramids, cones and solids of rotation, Dolomites Res. Notes Approx. DRNA 6 (2013), 20--26 (with S. De Marchi).

    2012

  33. Subperiodic trigonometric interpolation and quadrature, Appl. Math. Comput. 218 (2012), 10630--10638 (with L. Bos).
  34. On the generation of symmetric Lebesgue-like points in the triangle, J. Comput. Appl. Math. 236 (2012), 4925--4932 (with F. Rapetti, A. Sommariva).
  35. Trigonometric Gaussian quadrature on subintervals of the period, Electron. Trans. Numer. Anal. 39 (2012), 102--112 (with G. Da Fies).
  36. Algebraic cubature on planar lenses and bubbles, Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12 (with G. Da Fies).
  37. Computing Fekete and Lebesgue points: simplex, square, disk, J. Comput. Appl. Math. 236 (2012), 2477--2486 (with M. Briani, A. Sommariva).
  38. Low cardinality admissible meshes on quadrangles, triangles and disks, Math. Inequal. Appl. 15 (2012), 229--235 (with L. Bos).
  39. The "phase function" method to solve second-order asymptotically polynomial differential equations, Numer. Math. 121 (2012), 565--586 (with R. Spigler).

    2011

  40. Geometric Weakly Admissible Meshes, Discrete Least Squares Approximations and Approximate Fekete Points, Math. Comp. 80 (2011), 1601--1621 (with L. Bos, J.P. Calvi, N. Levenberg, A. Sommariva).
  41. On Multivariate Newton Interpolation at Discrete Leja Points, Dolomites Res. Notes Approx. DRNA 4 (2011), 15--20 (with L. Bos, S. De Marchi, A. Sommariva).
  42. Polynomial interpolation and cubature over polygons, J. Comput. Appl. Math. 235 (2011), 5232--5239 (with M. Gentile, A. Sommariva).
  43. An algebraic cubature formula on curvilinear polygons, Appl. Math. Comput. 217 (2011), 10003--10015 (with G. Santin, A. Sommariva).
  44. Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave, Numer. Algorithms 56 (2011), 45--60 (with M. Caliari, S. De Marchi, A. Sommariva).
  45. Weakly Admissible Meshes and Discrete Extremal Sets, Numer. Math. Theory Methods Appl. 4 (2011), 1--12 (with L. Bos, S. De Marchi, A. Sommariva).

    2010

  46. Computing multivariate Fekete and Leja points by numerical linear algebra, SIAM J. Numer. Anal. 48 (2010), 1984--1999 (with L. Bos, S. De Marchi, A. Sommariva).
  47. Analytic transformations of admissible meshes, East J. Approx. 16 (2010), 313--322 (with F. Piazzon).
  48. Least-squares polynomial approximation on weakly admissible meshes: disk and triangle, J. Comput. Appl. Math. 235 (2010), 660--668 (with L. Bos, A. Sommariva).
  49. On simple approximations to simple curves, Dolomites Res. Notes Approx. DRNA 3 (2010), 1--6 (with L. Bos).
  50. Approximate Fekete points for weighted polynomial interpolation, Electron. Trans. Numer. Anal. 37 (2010), 1--22 (with A. Sommariva).

    2009

  51. Gauss-Green cubature and moment computation over arbitrary geometries, J. Comput. Appl. Math. 231 (2009), 886--896 (with A. Sommariva).
  52. A numerical code for fast interpolation and cubature at the Padua points, Proceedings of the 9th CMMSE (2009), Vol. I, 218--228 (with M. Caliari, S. De Marchi, A. Sommariva).
  53. A massively parallel exponential integrator for advection-diffusion models, J. Comput. Appl. Math. 231 (2009), 82--91 (with L. Bergamaschi, M. Caliari, A. Martinez).
  54. Computing approximate Fekete points by QR factorizations of Vandermonde matrices, Comput. Math. Appl. 57 (2009), 1324--1336 (with A. Sommariva).
  55. New cubature formulae and hyperinterpolation in three variables, BIT Numerical Mathematics 49 (2009), 55--73 (with S. De Marchi, Y. Xu).

    2008

  56. Algorithm 886: Padua2D: Lagrange Interpolation at Padua Points on Bivariate Domains, ACM Trans. Math. Software 35-3 (2008) (with M. Caliari, S. De Marchi).
  57. Nontensorial Clenshaw-Curtis cubature, Numer. Algorithms 49 (2008), 409--427 (with A. Sommariva, R. Zanovello).
  58. Hyperinterpolation in the cube, Comput. Math. Appl. 55 (2008), 2490--2497 (with M. Caliari, S. De Marchi).
  59. Bivariate Lagrange interpolation at the Padua points: computational aspects, J. Comput. Appl. Math. 221 (2008), 284--292 (with M. Caliari, S. De Marchi).
  60. Meshless cubature over the disk by Thin-Plate Splines, J. Comput. Appl. Math. 221 (2008) 430--436 (with A. Punzi and A. Sommariva).
  61. Asymptotic approximations for second-order linear difference equations in Banach algebras, II, J. Math. Anal. Appl. 340 (2008), 433--450 (with T. Solda`, R. Spigler).
  62. Asymptotic approximations for second-order linear difference equations in Banach algebras, I, J. Math. Anal. Appl. 337 (2008), 1158--1170 (with T. Solda`, R. Spigler).

    2007

  63. Bivariate Lagrange interpolation at the Padua points: the ideal theory approach, Numer. Math. 108 (2007), 43--57 (with L. Bos, S. De Marchi, Y. Xu).
  64. Product Gauss cubature over polygons based on Green's integration formula, BIT Numerical Mathematics 47 (2007), 441--453 (with A. Sommariva).
  65. The LEM exponential integrator for advection-diffusion-reaction equations, J. Comput. Appl. Math. 210 (2007), 56--63 (with L. Bergamaschi, M. Caliari).
  66. Hyperinterpolation on the square, J. Comput. Appl. Math. 210 (2007), 78--83 (with M. Caliari, S. De Marchi).
  67. Liouville-Green asymptotic approximation for a class of matrix differential equations and semi-discretized partial differential equations, J. Math. Anal. Appl. 325 (2007), 69--89 (with R. Spigler).

    2006

  68. Bivariate Lagrange interpolation at the Padua points: the generating curve approach, J. Approx. Theory 143 (2006), 15--25 (with L. Bos, M. Caliari, S. De Marchi, Y. Xu).
  69. Meshless cubature by Green's formula, Appl. Math. Comput. 183 (2006), 1098--1107 (with A. Sommariva).
  70. Hyper2d: a numerical code for hyperinterpolation on rectangles, Appl. Math. Comput. 183 (2006), 1138--1147 (with M. Caliari, S. De Marchi, R. Montagna).
  71. Bivariate interpolation at Xu points: results, extensions and applications, Electron. Trans. Numer. Anal. 25 (2006), 1--16 (with L. Bos, M. Caliari, S. De Marchi).
  72. On the Lebesgue constant for the Xu interpolation formula, J. Approx. Theory 141 (2006), 134--141 (with L. Bos, S. De Marchi).
  73. Comparing Krylov and Leja approximations of large scale matrix exponentials, Springer LNCS vol. 3994, part IV, 2006 (Proc. of ICCS 2006, Reading, UK), 685-692 (with L. Bergamaschi, M. Caliari, A. Martinez).
  74. A numerical study of the Xu polynomial interpolation formula in two variables, Computing 76 (2006), 311--324 (with L. Bos, M. Caliari, S. De Marchi).
  75. Numerical cubature on scattered data by radial basis functions, Computing 76 (2006), 295--310 (with A. Sommariva).
  76. Liouville-Green asymptotics for almost-diagonal second-order matrix differential equations, Asymptotic Analysis 48 (2006), 267--294 (with R. Spigler).

    2005

  77. Bivariate polynomial interpolation on the square at new nodal sets, Appl. Math. Comput. 165 (2005), 261--274 (with M. Caliari, S. De Marchi).
  78. Adaptive bivariate Chebyshev approximation, Numer. Algorithms 38 (2005), 79--94 (with A. Sommariva, R. Zanovello).
  79. A parallel exponential integrator for large-scale discretizations of advection-diffusion models, Springer LNCS vol. 3666, 2005 (Proc. of Euro PVM MPI 2005, Sorrento, Italy), 483-492 (with L. Bergamaschi, M. Caliari, A. Martinez).

    2004

  80. The ReLPM exponential integrator for FE discretizations of advection-diffusion equations, Springer LNCS vol. 3039, part IV, 2004 (Proc. of ICCS 2004, Krakow, Poland), 434--442 (with L. Bergamaschi, M. Caliari).
  81. Adaptive bivariate Chebyshev approximation and efficient evaluation of integral operators, Appl. Numer. Anal. Comput. Math. 1 (2004), 115--121 (with A. Mardegan, A. Sommariva, R. Zanovello).
  82. Interpolating discrete advection-diffusion propagators at Leja sequences, J. Comput. Appl. Math. 172 (2004), 79--99 (with L. Bergamaschi, M. Caliari).

    2003

  83. Fast evaluation of discrete integral transforms by Chebyshev and Leja polynomial approximation, Constructive theory of functions, 347--353, DARBA, Sofia, 2003 (with S. De Marchi).
  84. Efficient approximation of the exponential operator for discrete 2D advection-diffusion problems, Numer. Linear Algebra Appl. 10 (2003), 271--289 (with L. Bergamaschi, M. Caliari).

    2001

  85. Approximating the approximant: a numerical code for polynomial compression of discrete integral operators, In memory of W. Gross. Numer. Algorithms 28 (2001), 101--116 (with S. De Marchi).
  86. Fast summation of power series with coefficients analytic at infinity, Numer. Algorithms 27 (2001), 77--87 (with A. Sommariva, R. Zanovello).
  87. Positive multiplication preserves dissipativity in commutative C*-algebras, J. Inequal. Appl. 6 (2001), 247--251 (with A. Sommariva).

    2000

  88. Chebyshev-like compression of linear and nonlinear discretized integral operators, Neural Parallel Sci. Comput. 8 (2000), 327--353.
  89. Computing positive fixed-points of decreasing Hammerstein operators by relaxed iterations, J. Integral Equations Appl. 12 (2000), 95--112 (with A. Sommariva).
  90. Relaxed Picard-like methods for nonlinear integral equations arising in transport theory, Applied and industrial mathematics, Venice--2, 1998, 273--285, Kluwer Acad. Publ., Dordrecht, 2000 (with E. Facchinello, A. Sommariva).
  91. Efficient computation of the exponential operator for large, sparse, symmetric matrices, Numer. Linear Algebra Appl. 7 (2000), 27--45 (with L. Bergamaschi).
  92. A new summation method for power series with rational coefficients, Math. Comp. 69 (2000), 749--756 (with S. Dassie`, R. Zanovello).
  93. A variant of the complex Liouville-Green approximation theorem, Arch. Math. (Brno) 36 (2000), 213--218 (with R. Spigler).
  94. Existence of positive continuous solutions of perturbed Hammerstein equations, Appl. Anal. 74 (2000), 429--438.
  95. Constructive approximation for a class of perturbed Hammerstein integral equations, Nonlinear Anal. 41 (2000), Ser. A: Theory Methods, 177--185 (with A. Sommariva).

    1999

  96. Liouville-Green-Olver approximations for complex difference equations, J. Approx. Theory 96 (1999), 301--322 (with F. Locatelli, R. Spigler).
  97. Constructive analysis of purely integral Boltzmann models, J. Integral Equations Appl. 11 (1999), 393--404 (with A. Sommariva).
  98. On the complex differential equation Y"+G(z)Y=0 in Banach algebras, Stud. Appl. Math. 102 (1999), 291--308 (with R. Spigler).

    1998

  99. Asymptotic summation of power series, Numer. Math. 80 (1998), 61--73 (with S. Dassie`, R. Zanovello).
  100. Approximating fixed-points of decreasing operators in spaces of continuous functions, Numer. Funct. Anal. Optim. 19 (1998), 635--646 (with A. Sommariva).
  101. A survey on the Liouville-Green (WKB) approximation for linear difference equations of the second order, Advances in Difference Equations: Proceedings of the Second International Conference on Difference Equations (Veszprem, 1995), 567--577, CRC Press, 1998 (with R. Spigler).

    1997

  102. Peano's kernel theorem for vector-valued functions: a weak version in normed spaces, Numer. Funct. Anal. Optim. 18 (1997), 65--74 (with S. De Marchi).

    1996

  103. Peano's kernel theorem for vector-valued functions and some applications, Numer. Funct. Anal. Optim. 17 (1996), 57--64 (with S. De Marchi).
  104. Asymptotic representation for the Blumenthal-Nevai orthogonal polynomials in the essential spectrum, Methods Appl. Anal. 3 (1996), 457--475 (with R. Spigler).
  105. WKB-type approximations for second-order differential equations in C*-algebras, Proc. Amer. Math. Soc. 124 (1996), 1763--1771 (with R. Spigler).

    1995

  106. Convergence analysis of the semi-implicit Euler method for abstract evolution equations, Numer. Funct. Anal. Optim. 16 (1995), 785--803 (with R. Spigler).
  107. On some connections between well-posedness and general properties of numerical methods, Z. Angew. Math. Mech. 75 (1995), 237--241 (with R. Zanovello).
  108. On regularity at t=0 for semilinear ADEs and its numerical applications, Semigroup Forum 50 (1995), 97--104.

    1994

  109. Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems, Mathematics of Computation 1943--1993: a half-century of computational mathematics (Vancouver, BC, 1993), 281--285, Proc. Sympos. Appl. Math., 48, Amer. Math. Soc., Providence, RI, 1994 (with S. De Marchi, R. Zanovello).
  110. Semi-implicit discretization of abstract evolution equations, Equadiff 8 (Bratislava, 1993), Tatra Mt. Math. Publ. 4 (1994), 207--212 (with R. Spigler).
  111. Discrete and continuous Liouville-Green-Olver approximations: a unified treatment via Volterra-Stieltjes integral equations, SIAM J. Math. Anal. 25 (1994), 720--732 (with R. Spigler).

    1993

  112. Cesaro's theorems for complex sequences, J. Math. Anal. Appl. 180 (1993), 317--324 (with R. Spigler).
  113. Abstract versions of L'Hopital's rule for holomorphic functions in the framework of complex B-modules, J. Math. Anal. Appl. 180 (1993), 17--28 (with R. Spigler).
  114. Extending L'Hopital's theorem to B-modules, J. Math. Anal. Appl. 179 (1993), 638--645 (with R. Spigler).
  115. Finite moments perturbations of y"=0 in Banach algebras, Proc. Amer. Math. Soc. 119 (1993), 97--103 (with R. Spigler).
  116. A generalization of l'Hopital's rule via absolute continuity and Banach modules, Real Anal. Exchange 18 (1992/93), 557--567.

    1992

  117. Extensions and numerical applications of the Liouville-Green approximation, Ph.D. Thesis, Doctoral School in Computational Mathematics, Italian North-Eastern Consortium (Universities of Bologna, Padova, Trieste and Udine), 1--84
  118. On the superlinear convergence of the secant method, Amer. Math. Monthly 99 (1992), 758--761 (with R. Zanovello).
  119. Liouville-Green 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), 105--116 (with R. Spigler).
  120. Improved estimates for the derivatives of the O-symbols in view of numerical applications, J. Math. Anal. Appl. 164 (1992), 480--488 (with R. Spigler).
  121. WKBJ-type approximation for finite moments perturbations of the differential equation y"=0 and the analogous difference equation, J. Math. Anal. Appl. 169 (1992), 437--452 (with R. Spigler).

    1991

  122. Global existence and uniqueness for the Kummer transformation problem subject to non-Cauchy data, Differential Integral Equations 4 (1991), 991--1003 (with R. Spigler).

    1990

  123. A numerical method for evaluating zeros of solutions of second-order linear differential equations, Math. Comp. 55 (1990), 591--612 (with R. Spigler).
  124. Approximating zeros of solutions of second-order linear ODEs by "phase function" methods, Asymptotic and computational analysis (Winnipeg, MB, 1989), 707--722, Lecture Notes in Pure and Appl. Math., 124, Dekker, New York, 1990 (with R. Spigler).

selected citations

citations in books (the numbers refer to the list above)
citations in state of the art surveys

Didactic curriculum

at the University of Padova, from 1991

see also the web page devoted to students: www.math.unipd.it/~marcov/studenti.html

Teaching (74 courses)
(o): full course responsibility
(%): teaching assistantship or co-teaching

at the Faculty of Science

at the Faculty of Engineering

Written tutorials (in Italian)

Ph.D. courses

Talks on didactics

Supervision and organization