References

Prescribed text

1.

Burden, R. L., and Faires, J. D. (2011), Numerical Analysis (9th ed.), Boston, Brooks/Cole, Cengage Learning.

Other texts

1.

Atkinson, K. E. (1989), An Introduction to Numerical Analysis (2nd ed.), New York, Wiley.

2.

Kincaid, D., and Cheney, W. (2002), Numerical Analysis: Mathematics of Scientific Computing (3rd ed.), Pacific Grove, CA, Brooks/Cole.

3.

Süli, E., and Mayers, D. F. (2003), An Introduction to Numerical Analysis, Cambridge, Cambridge University Press.

4.

Higham, N. J. (2002), Accuracy and Stability of Numerical Algorithms (2nd ed.), Philadelphia, SIAM.

Further reading

1.

Aitken, A. C. (1926), On Bernoulli’s numerical solution of algebraic equations, Proceedings of the Royal Society of Edinburgh, 46, 289–305.

2.

Benoit, Commandant (1924), Note sur une méthode de résolution des équations normales (Procédé du Commandant Cholesky), Bulletin Géodésique, 2, 67–77.

3.

Dowell, M., and Jarratt, P. (1971), A modified regula falsi method for computing the root of an equation, BIT Numerical Mathematics, 11, 168–174.

4.

Euler, L. (1768), Institutionum Calculi Integralis, Vol. I, St Petersburg, Imperial Academy of Sciences.

5.

Gauss, C. F. (1809), Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium, Hamburg, Perthes and Besser.

6.

Goldberg, D. (1991), What every computer scientist should know about floating-point arithmetic, ACM Computing Surveys, 23, 5–48.

7.

Horner, W. G. (1819), A new method of solving numerical equations of all orders, by continuous approximation, Philosophical Transactions of the Royal Society of London, 109, 308–335.

8.

IEEE (1985), IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Std 754-1985, New York, Institute of Electrical and Electronics Engineers.

9.

Jacobi, C. G. J. (1845), Über eine neue Auflösungsart der bei der Methode der kleinsten Quadrate vorkommenden linearen Gleichungen, Astronomische Nachrichten, 22, 297–306.

10.

Kahan, W. (1958), Gauss–Seidel Methods of Solving Large Systems of Linear Equations, Ph.D. thesis, University of Toronto.

11.

Kutta, W. (1901), Beitrag zur näherungsweisen Integration totaler Differentialgleichungen, Zeitschrift für Mathematik und Physik, 46, 435–453.

12.

Lagrange, J. L. (1795), Leçons élémentaires sur les mathématiques, Journal de l’École Polytechnique, 2, 173–278.

13.

Muller, D. E. (1956), A method for solving algebraic equations using an automatic computer, Mathematical Tables and Other Aids to Computation, 10, 208–215.

14.

Newton, I. (1711), De analysi per aequationes numero terminorum infinitas, London (written 1669).

15.

Ostrowski, A. M. (1954), On the linear iteration procedures for symmetric matrices, Rendiconti di Matematica e delle sue Applicazioni, 13, 140–163.

16.

Raphson, J. (1690), Analysis Aequationum Universalis, London.

17.

Richardson, L. F. (1911), The approximate arithmetical solution by finite differences of physical problems involving differential equations, Philosophical Transactions of the Royal Society of London, Series A, 210, 307–357.

18.

Romberg, W. (1955), Vereinfachte numerische Integration, Det Kongelige Norske Videnskabers Selskab Forhandlinger, 28, 30–36.

19.

Runge, C. (1895), Über die numerische Auflösung von Differentialgleichungen, Mathematische Annalen, 46, 167–178.

20.

Runge, C. (1901), Über empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten, Zeitschrift für Mathematik und Physik, 46, 224–243.

21.

Schoenberg, I. J. (1946), Contributions to the problem of approximation of equidistant data by analytic functions, Quarterly of Applied Mathematics, 4, 45–99 and 112–141.

22.

Seidel, L. (1874), Über ein Verfahren, die Gleichungen, auf welche die Methode der kleinsten Quadrate führt, sowie lineäre Gleichungen überhaupt, durch successive Annäherung aufzulösen, Abhandlungen der Bayerischen Akademie der Wissenschaften, 11, 81–108.

23.

Simpson, T. (1743), Mathematical Dissertations on a Variety of Physical and Analytical Subjects, London.

24.

Steffensen, J. F. (1933), Remarks on iteration, Skandinavisk Aktuarietidskrift, 16, 64–72.

25.

Taylor, B. (1715), Methodus Incrementorum Directa et Inversa, London.

26.

Wilkinson, J. H. (1963), Rounding Errors in Algebraic Processes, Englewood Cliffs, NJ, Prentice-Hall.

27.

Young, D. M. (1954), Iterative methods for solving partial difference equations of elliptic type, Transactions of the American Mathematical Society, 76, 92–111.