Papers by subject

Approximation Theory & Numerical Analysis

• 1.  On the condition number of Newton interpolation: Chebyshev points and monotonically ordering.  Journal of Approximation Theory, vol. 287, 105867  (2023) 

  2.  A Chebyshev-A. Markov-Stieltjes-separation-type theorem for classical Romberg quadrature.  Numerical Algorithms, vol. 92, 2365-2376 (2023)

  3. Backward and forward stability analysis of Neville's algorithm for interpolation and a pyramid algorithm for the computation of Lebesgue functions. Numerical Algorithms, vol. 89, 1521-1531  (2022)

  4. A divergent sequence of Romberg integrals. Results in Mathematics, vol. 75,  11  (2020)

  5. Rounding error analysis of divided differences schemes: Newton's divided differences; Neville's algorithm; Richardson extrapolation; Romberg integration; etc. Numerical Algorithms, vol. 85, 591-606  (2020)

  6.  On the numerical stability of Newton’s formula for Lagrange interpolation.  Journal of Computational and Applied Mathematics, vol. 365 112369  (2020)

  7. An exponential lower bound for the condition number of real Vandermonde matrices. Applied Numerical Mathematics, vol. 128, 81-83 (2018)

  8. The stability of extended Floater-Hormann interpolants. Numerische Mathematik, vol. 136, 287-313 (2017) w/W. Mascarenhas.

  9. The effects of rounding errors in the nodes on barycentric interpolation. Numerische Mathematik, vol. 135, 113-141 (2017) w/W. Mascarenhas.

  10. A comparison between extended Floater-Hormann interpolants and trigonometric interpolation. Dolomites Research Notes on Approximation, vol. 10 (1), 23-32 (2017)

  11. On the numerical stability of Floater-Hormann's rational interpolant.  Numerical Algorithms, vol. 72, 131-152 (2016)

  12. A few remarks on ``On certain Vandermonde determinants whose variables separate".  Dolomites Research Notes on Approximation, vol. 8 (1), 1-11 (2015) w/S. De Marchi.

  13. On the backward stability of the second barycentric formula for interpolation.  Dolomites Research Notes on Approximation, vol. 7 (1), 1-12   (2014) w/W. Mascarenhas.

 Linear Algebra  & Determinant Theory

1. Replacing minors by linear functions and products in the Cauchy-Sylvester compound and Adjugate determinants. Linear and Multilinear Algebra, vol. 70 (5), 909-918 (2022), w/F. S. Alves.

2. A note on linearly dependent symmetric matrices. Linear and Multilinear Algebra, vol. 69 (13), 2539-2545  (2021),  w/G. Haeser.

3. Schur functions through Lagrange polynomials. Journal of Pure and Applied Algebra, vol. 220 (8),  2948-2954 (2016)

4. Can Sylvester's determinantal identity, equivalently Muir's law of extensible minors be generalized? Linear  Algebra and its Applications, vol. 481, 70-83 (2015), w/F. S. Alves.

5. On some determinantal identities formation laws.  Linear and Multilinear Algebra, vol. 63 (9), 1760-1767 (2015)

6. A generalization of Mühlbach's extension principle for determinantal identities.  Linear and Multilinear Algebra, vol. 61 (10), 1363-1376 (2013)

 Number Theory

1. Sharp estimates for the Möbius function with coprimality restrictions. Mathematics of Computation https://doi.org/10.1090/mcom/4128 .

2. On the maximal zero-free half-planes of the  Hurwitz zeta function. Research in Number Theory (to appear).

3. A generalization of Landau's identities for B-free integers. Submitted.

4. Weighted summation of Dirichlet convolutions and applications to some divisor problems over  k-free and B-free integers. Integers, vol. 24, A75 (2024)

5. On fast converging sequences for constants of Bendersky type: Stirling,  Glaisher--Kinkelin, Bendersky--Adamchik and some others. Dolomites Research Notes on Approximation, vol. 17 (1), 32-39 (2024)

6. Constant components of the Mertens function and its connections with Tschebyschef's theory for counting prime numbers II. Bulletin of the Brazilian Mathematical Society, vol. 55, 24   (2024),  w/P. A. Martin.

7. The Dirichlet divisor problem over square-free integers and unitary convolutions. Notes on Number Theory and Discrete Mathematics, vol. 29 (3), 549-556 (2023)

8. Two generalizations of Liouville $\lambda$ function. Notes on Number Theory and Discrete Mathematics, vol. 29 (1), 30-39 (2023).

9. Constant components of the Mertens function and its connections with Tschebyschef's theory for counting prime numbers.  Bulletin of the Brazilian Mathematical Society, vol. 53, 501-522   (2022),  w/P. A. Martin.

10. Dirichlet matrices: determinants, permanents and the Factorisatio Numerorum problem. Linear  Algebra and its Applications, vol. 628, 115-129 (2021)

11. A few remarks on the values of the Bernoulli polynomials at rational arguments and some relations with ζ(2k + 1). Notes on Number Theory and Discrete Mathematics, vol. 27 (4), 180-186   (2021),  w/G. C. O.  Teruya.

 Short Fun Papers & Mathematics Education

1. A short proof for the volume of square pyramids. The American Mathematical Monthly, vol. 129 (8), 784 (2022)

2. A New proof of the equivalence of the Cauchy mean value theorem and the mean value theorem. The American Mathematical Monthly, vol. 127 (5), 460 (2020)

3. A proof of the Schwarz theorem on mixed partial derivatives via elementary approximation theory. Elemente der Mathematik, vol. 75 (3),  125-128  (2020)

4. A Straightforward Approach to the Product Rule. The American Mathematical Monthly, vol 126 (8), 754 (2019)

5. The geometric Mean Value Theorem.  International Journal of Mathematics education in Science and Engineering, vol. 49 (4), 613-615  (2018)