References

Autore/Autrice
Affiliazione

Enrico Bertolazzi

University of Trento, Department of Industrial Engineering

[1]
2025. NIST digital library of mathematical functions. Retrieved from https://dlmf.nist.gov/
[2]
Milton Abramowitz and Irene A. Stegun (Eds.). 1964. Handbook of mathematical functions with formulas, graphs, and mathematical tables. National Bureau of Standards, Washington, D.C. Retrieved from https://personal.math.ubc.ca/~cbm/aands/
[3]
G. E. Alefeld, F. A. Potra, and Yixun Shi. 1995. Algorithm 748: Enclosing zeros of continuous functions. ACM Transactions on Mathematical Software 21, 3 (1995), 327–344. https://doi.org/10.1145/210089.210111
[4]
Bernhard Beckermann. 2000. The condition number of real vandermonde, krylov and positive definite hankel matrices. Numerische Mathematik 85, 4 (2000), 553–577. https://doi.org/10.1007/PL00005392
[5]
A. Berman and R. J. Plemmons. 1994. Nonnegative matrices in the mathematical sciences. SIAM.
[6]
Roberto Bevilacqua, Dario Bini, Milvio Capovani, and Ornella Menchi. 1992. Metodi numerici. Zanichelli.
[7]
Åke Björck. 1996. Numerical methods for least squares problems. SIAM.
[8]
Richard P. Brent. 1973. Algorithms for minimization without derivatives. Prentice-Hall, Englewood Cliffs, NJ.
[9]
J. C. P. Bus and T. J. Dekker. 1975. Two efficient algorithms with guaranteed convergence for finding a zero of a function. ACM Transactions on Mathematical Software 1, 4 (1975), 330–345. https://doi.org/10.1145/355656.355659
[10]
J. C. Butcher. 1987. The numerical analysis of ordinary differential equations : Runge-kutta and general linear methods (First ed.). Wiley, Chichester.
[11]
Frank Cameron. 2006. A matlab package for automatically generating runge-kutta trees, order conditions, and truncation error coefficients. ACM Trans. Math. Softw. 32, 2 (June 2006), 274–298. https://doi.org/10.1145/1141885.1141892
[12]
Tirupathi R. Chandrupatla. 1997. A new hybrid quadratic/bisection algorithm for finding the zero of a nonlinear function without using derivatives. Advances in Engineering Software 28, 3 (1997), 145–149. https://doi.org/10.1016/S0965-9978(96)00051-8
[13]
Theodore S. Chihara. 1978. An introduction to orthogonal polynomials. Gordon; Breach, New York.
[14]
T. J. Dekker. 1969. Finding a zero by means of successive linear interpolation. In Constructive aspects of the fundamental theorem of algebra, B. Dejon and P. Henrici (eds.). Wiley-Interscience, London, 37–48.
[15]
Carl Friedrich Gauss. 1814. Methodus nova integralium valores per approximationem inveniendi. Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores 3, (1814).
[16]
Gene H. Golub and Charles F. Van Loan. 1989. Matrix computations. Johns Hopkins Univ. Press.
[17]
Gene H. Golub and John H. Welsch. 1969. Calculation of gauss quadrature rules. Mathematics of Computation 23, 106 (1969), 221–230. https://doi.org/10.2307/2004418
[18]
L. A. Hageman and D. M. Young. 1981. Applied iterative methods. Academic Press.
[19]
W. W. Hager. 1988. Applied numerical linear algebra. Prentice Hall.
[20]
E. Hairer, S. P. Nørsett, and G. Wanner. 1993. Solving ordinary differential equations i: Nonstiff problems (2nd ed.). Springer.
[21]
Ernst Hairer and Gerhard Wanner. 1996. Solving ordinary differential equations II: Stiff and differential-algebraic problems (2nd ed.). Springer-Verlag, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05221-7
[22]
Nicholas J. Higham. 2002. Accuracy and stability of numerical algorithms (2nd ed.). SIAM, Philadelphia, PA.
[23]
R. A. Horn and C. R. Johnson. 2012. Matrix analysis (2nd ed.). Cambridge University Press.
[24]
Alston S. Householder. 1970. The numerical treatment of a single nonlinear equation. McGraw-Hill, New York.
[25]
Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, and Adrienne S. Lavine. 2006. Fundamentals of heat and mass transfer (6th ed.). John Wiley & Sons.
[26]
Carl Gustav Jacob Jacobi. 1826. Ueber gauß’ neue methode, die werthe der integrale näherungsweise zu finden. Journal für die reine und angewandte Mathematik 1, (1826), 301–308. Retrieved from https://eudml.org/doc/183033
[27]
S. Lang and I. Mencattini. 2014. Algebra lineare. Bollati Boringhieri.
[28]
Adrien-Marie Legendre. 1785. Recherches sur l’attraction des sphéroïdes homogènes. Mémoires de Mathématiques et de Physique, présentés à l’Académie Royale des Sciences par divers savans 10, (1785), 411–435.
[29]
I. F. D. Oliveira and R. H. C. Takahashi. 2021. An enhancement of the bisection method average performance preserving minmax optimality. ACM Transactions on Mathematical Software 47, 1 (2021), 1–24. https://doi.org/10.1145/3423597
[30]
J. M. Ortega. 1987. Matrix theory (a second course). Plenum Press.
[31]
J. M. Ortega and W. C. Rheinboldt. 1970. Iterative solution of nonlinear equations in several variables. Academic Press.
[32]
William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. 2007. Numerical recipes: The art of scientific computing (3rd ed.). Cambridge University Press, Cambridge.
[33]
A. Quarteroni, F. Saleri, and P. Gervasio. 2017. Calcolo scientifico: Esercizi e problemi risolti con MATLAB e octave. Springer Milan.
[34]
C. Ridders. 1979. A new algorithm for computing a single root of a real continuous function. IEEE Transactions on Circuits and Systems 26, 11 (1979), 979–980. https://doi.org/10.1109/TCS.1979.1084580
[35]
Adel S. Sedra, Kenneth C. Smith, Tony Chan Carusone, and Vincent Gaudet. 2020. Microelectronic circuits (8th ed.). Oxford University Press.
[36]
J. M. Smith, H. C. Van Ness, Michael M. Abbott, and M. T. Swihart. 2005. Introduction to chemical engineering thermodynamics (7th ed.). McGraw-Hill Education.
[37]
Thomas Joannes Stieltjes. 1894. Recherches sur les fractions continues. Annales de la Faculté des sciences de Toulouse, 1re série 8, 4 (1894), J1–J122. Retrieved from https://www.numdam.org/item/AFST_1894_1_8_4_J1_0
[38]
J. Stoer and R. Bulirsch. 1975. Introduzione all’ analisi numerica. Zanichelli.
[39]
Gábor Szegő. 1939. Orthogonal polynomials. American Mathematical Society, Providence, RI.
[40]
Pafnouti L. Tchebichef. 1858. Sur les fractions continues. Journal de Mathématiques Pures et Appliquées, 2e série 3, (1858), 289–323. Retrieved from https://numdam.org/item/JMPA_1858_2_3__289_0/
[41]
Joseph F. Traub. 1964. Iterative methods for the solution of equations. Prentice-Hall, Englewood Cliffs, NJ.
[42]
Lloyd N. Trefethen and David Bau. 1997. Numerical linear algebra. SIAM.
[43]
R. S. Varga. 2000. Matrix iterative analysis (2nd ed.). Springer. https://doi.org/10.1007/978-3-642-05156-2
[44]
Frank M. White. 2011. Fluid mechanics (7th ed.). McGraw-Hill Education.
[45]
Z. I. Woźnicki. 1994. Nonnegative splitting theory. Japan Journal of Industrial and Applied Mathematics 11, 2 (1994), 289–342. https://doi.org/10.1007/BF03167226