Staff profile

Dr Alan Andrew

Emeritus Scholar

Faculty of Science, Technology and Engineering

School of Engineering and Mathematical Sciences
Department of Mathematics and Statistics

Physical Sciences 2, Room 329, Melbourne (Bundoora)

 

Qualifications

MSc (NZ), MSc (ANU), PhD (La Trobe), FIMA, FAustMS

Membership of professional Associations

Fellow of the Institute of Mathematics and its Applications (UK), Fellow of the Australian Mathematical Society.

Area of study

Mathematics and Statistics

Brief Profile

Dr. Andrew works on development and analysis of numerical methods for the solution of eigenvalue problems, especially inverse Sturm-Liouville problems and sensitivity problems for matrix eigenvectors.

Associate Editor, Bulletin of the Australian Mathematical Society: 1979-2002.

Editorial Board member, Linear Algebra with Applications: 2007-2009.

Dr. Andrew is a regular referee for numerous international journals and a reviewer for Mathematical Reviews and the Zentralblatt MATH (over 500 reviews so far).

Research specialisation

- Numerical methods

Recent Publications

Alan L. Andrew "Finite difference methods for half inverse Sturm-Liouville problems", Appl. Math. Comput. 218 (2011) 445-457.

Alan L. Andrew "Inverse Sturm-Liouville problems: some recent developments", ANZIAM J. 52(CTAC2010) (2011) C287-C302.

Alan L. Andrew, P. H. Foo, Roger C. E. Tan and Markus Wachter, “Acceleration of inexact inverse iteration for eigenvalue problems”, ANZIAM J 50 (2008) C237-C250.

Alan L. Andrew “Computing Sturm-Liouville potentials from two spectra”, Inverse Problems 22 (2006) 2069-2081.

Alan L. Andrew “Asymptotic correction and inverse eigenvalue problems: an overview”,  ANZIAM J. E46 (2005) C1-C14.

Alan L. Andrew “Numerov’s method for inverse Sturm-Liouville problems”, Inverse Problems 21 (2005) 223-238.

Alan L. Andrew "Numerical solution of inverse Sturm-Liouville problems", ANZIAM J. 45E (2004) C326-C337.

Alan L. Andrew “Asymptotic correction of more Sturm-Liouville estimates”, BIT 43 (2003) 485-503.

Alan L. Andrew "Asymptotic correction of Numerov's eigenvalue estimates with general boundary conditions", ANZIAM J. 44E (2003) C1-C19.

Alan L. Andrew and Roger C.E. Tan "Iterative computation of higher derivatives of repeated eigenvalues and the corresponding eigenvectors", Operator Theory: Advances and Applications 130 (2001) 43-54.

Alan L. Andrew and Roger C.E. Tan "Iterative computation of derivatives of repeated eigenvalues and the corresponding eigenvectors", Numer. Linear Algebra Appl. 7 (2000) 151.167.

Alan L. Andrew "Asymptotic correction of Numerov's eigenvalue estimates with natural boundary conditions", J. Comput. Appl. Math.,125 (2000) 359-366.

Alan L. Andrew and Roger C.E. Tan "Computation of derivatives of repeated eigenvalues and the corresponding eigenvectrors of symmetric matrix pencils", SIAM J. Matrix Anal. Appl. 20 (1998) 78-100.

Alan L. Andrew "Finite and continuous perturbations of matrix eigenvalues" Appl. Math. Lett. 11(1) (1998) 47-51.

Alan L. Andrew "Centrosymmetric matrices" SIAM Rev. 40 (1998) 697-698.

Older Publications

Alan L. Andrew, "Twenty years of asymptotic correction for eigenvalue computation", ANZIAM J 42(E) (2000) C96-C116.

Alan L. Andrew, "Quadrature errors in finite element eigenvalue computations" ANZIAM J. 42 (2000) 136-140.

Alan L. Andrew, "Sensitivity problems for multiple eigenvalues in structural analysis", in Proc. 4th Biennial Engng. Math. Appl. Conf. EMAC2000 (R. L. May, G. F. FitzGerald and I. H. Grundy, eds) IEAust 2000. pp.51-54.

Alan L. Andrew and Roger C.E. Tan "Computation of mixed partial derivatives of eigenvalues and eigenvectors by simultaneous iteration" Commun. Numer. Meth. Engng. 15 (1999) 641-649.

Alan L. Andrew, "Iterative methods for computation of derivatives of eigenvalues and eigenvectors", in Proc. 3rd Biennial Engng. Math. Appl. Conf. EMAC'98 (J.A.K. Stott and E. O. Tuck eds.) IEAust 1998 pp 83-86.

Roger C. E. Tan and Alan L. Andrew, "Computing derivatives of eigenvectors corresponding to multiple eigenvalues of nonsymmetric matrix functions" in Proc. 8th Internat. Colloq. Differential Equations, Plovdiv, Bulgaria 1997 (D. Bainov ed.) Utrecht: VSP 1998, pp 409-414.

Alan L. Andrew, Computation of derivatives of eigenvalues and eigenvectors of parameter-dependent matrices", in Computational Techniques and Applications: CTAC-97 (B. J. Noye, M. D. Teubner and A.W. Gill, eds.), Singapore: World Scientific 1998, pp 51-58.

Alan L. Andrew and Roger C.E. Tan "Computation of derivatives of repeated eigenvalues and the corresponding eigenvectors" Z. Angew. Math. Mech. 76 (Suppl.2) (1996) 467-468.

Alan L. Andrew and Roger C.E. Tan "Computation of derivatives of repeated eigenvalues and corresponding eigenvectors by simultaneous iteration" AIAA J. 34 (1996) 2214-2216.

A.L. Andrew "Solution of nonlinear and multiparameter eigenvalue problems" in Computational Techniques and Applications:CTAC-95 ( R.L. May and A.K. Easton, eds) pp. 97-104, Singapore: World Scientific 1996.

A.L. Andrew, K.-W.E. Chu and P. Lancaster "On the numerical solution of nonlinear eigenvalue problems" Computing 55 (1995) 91-111.

Roger C. E. Tan and Alan L. Andrew, "Henrici's transformation and its application to the computation of derivatives of eigensystems", J. Comput. Appl. Math. 59 (1995), 1-8.

Alan L. Andrew, "Asymptotic correction of computed eigenvalues of differential equations", Ann. Numer. Math. 1 (1994), 41-51.

Roger C.E. Tan, Alan L. Andrew and Felicia M.L. Hong, "Iterative computation of second-order derivatives of eigenvalues and eigenvectors", Commun. Numer. Meth. Engng. 10 (1994) 1-9.

Alan L. Andrew, "Some recent developments in inverse eigenvalue problems", in Computational Techniques and Applications: CTAC-93 (D. Stewart, H. Gardner and D. Singleton, eds.) Singapore: World Scientific 1994, pp 94-102.

Alan L. Andrew, K.-W. Eric Chu and Peter Lancaster "Derivatives of eigenvalues and eigenvectors of matrix functions" SIAM J. Matrix Anal. Appl. 14 (1993) 903-926.

Alan L. Andrew, K-W. Eric Chu and Peter Lancaster, "Sensitivities of eigenvalues and eigenvectors of problems nonlinear in the eigenparameter", Appl. Math. Lett. 5(3) (1992) 69-72.

Alan L. Andrew, "Computing two-sided bounds for eigenvalues of differential equations", in Computational Techniques and Applications: CTAC-91 (J. Noye, B. Benjamin and L. Colgan, eds.) Adelaide, Comp. Math. Group AustMS 1992, pp 101-108.

Alan L. Andrew and K-W. Eric Chu, "Comments on 'Analytical solutions for the nth derivatives of eigenvalues and eigenvectors for a nonlinear eigenvalue problem' ", AIAA J. 29 (1991), 1182-1183.

Alan L. Andrew, " Eigenvalues and singular values of certain random matrices", J. Comput. Appl. Math. 30 (1990) 165-171.

Alan L. Andrew, Frank R. de Hoog and Roger C.E. Tan, "Direct computation of derivatives of eigenvalues and eigenvectors", Internat. J. Computer Math. 36 (1990) 251-255.

Alan L. Andrew, "Choosing test matrices for numerical software", in Computational Techniques and Applications: CTAC-89 (W.L. Hogarth and B.J. Noye eds.) New York: Hemisphere 1990, pp 561-567.

Roger C.E. Tan and Alan L. Andrew, "Computing derivatives of eigenvalues and eigenvectors by simultaneous iteration", IMA J. Numer. Anal. 9 (1989) 11-122.

Alan L. Andrew, "Correction of finite difference eigenvalues of periodic Sturm-Liouville problems", J. Austral. Math. Soc. (Series B) 30 (1989), 460-469.

Alan L. Andrew, "Correction of finite element eigenvalues for problems with natural or periodic boundary conditions", BIT 28 (1998) 254-269.

Alan L. Andrew, " Efficient computation of higher Sturm-Liouville eigenvalues", Internat. Ser. Numer. Math. (Birkhauser) 86 (1988) 1-9.

Alan L. Andrew, "Some recent developments in finite element eigenvalue computation", in Computational Techniques and Applications: CTAC-87 (J. Noye and C. Fletcher eds.) Amsterdam: North-Holland 1998, pp 83-91.

Alan L. Andrew and John W. Paine "Correction of finite element estimates for Sturm-Liouville eigenvalues" Numer. Math. 50 (1986) 205-215.

A. L. Andrew, "The accuracy of Numerov's method for eigenvalues", BIT 26 (1986) 251-253.

R.A.S. Fiedler and A.L. Andrew, "Finite element calculations for non-radial oscillations of stars", Austral. J. Phys. 39 (1986) 99-102.

Alan L. Andrew, "Asymptotic correction of finite difference eigenvalues", in Computational Techniques and Applications: CTAC-85 (J. Noye and R. May eds.) Amsterdam: North-Holland 1986, pp 333-341.

Alan L. Andrew and John W. Paine "Correction of Numerov's eigenvalue estimates" Numer. Math. 47 (1985) 289-300.

A. L. Andrew, "Further comments on 'On the eigenvectors of symmetric Toeplitz matrices' ", IEEE Trans. Acoust. Speech Signal Processing ASSP-33 (1985), 1013.

Alan L. Andrew, "Numerical solution of eigenvalue problems for ordinary differential equations", in Computational Techniques and Applications: CTAC-83 (J. Noye and C. Fletcher eds.) Amsterdam: North-Holland 1984, pp 8410852.

John W. Paine and Alan L. Andrew, "Bounds and higher-order estimates for Sturm-Liouville eigenvalues", J. Math. Anal. Appl. 96 (1983) 388-394.

Alan L Andrew, "Computation of higher Sturm-Liouville eigenvalues", Congressus Numerantium 34 (1982) 3-16.

Alan L. Andrew, Frank R. de Hoog and Peter J. Robb, "Leighton's bounds for Sturm-Liouville eigenvalues", J. Math. Anal. Appl. 83 (1981) 11-19.

A. L. Andrew, "Iterative computation of derivatives of eigenvalues and eigenvectors", J. Inst. Math. Appl. 24 (1979) 209-218.

Alan L. Andrew, "Convergence of an iterative method for derivatives of eigensystems", J. Computational Phys. 26 (1978) 107-112.

A. L. Andrew, "Existence and uniqueness regions for solutions of nonlinear equations", Bull. Austral. Math. Soc. 19 (1978) 277-282.

A.L. Andrew, S.A. Morris, G.P. Protomastro and P.J. Stacey, "On mixed partial derivatives", Austral. Math. Soc. Gazette 4 (1`977) 49-54.

A. L. Andrew, "Error bounds for the modified Newton's method", Bull. Austral. Math. Soc. 14 (1976) 427-433.

A.L. Andrew, "The mathematics of population growth", Math. Gazette 58 (1974) 272-276.

 Alan L. Andrew, "Eigenvectors of certain matrices", Linear Algebra Appl. 7 (1973) 151-162.

A. L. Andrew, "Solution of equations involving centrosymmetric matrices", Technometrics 15 (1973) 405-407.

Alan L. Andrew, "Variational Solution of certain nonlinear eigenvalue problems", Bull. Austral. Math. Soc. 5 (1971)137-138.

A.L. Andrew and G.C. Elton, "Computation of eigenvectors corresponding to multiple eigenvalues", Bull. Austral. Math. Soc. 4 (1971) 419-422.

Alan L. Andrew, "Variational solution of some nonlinear eigenvalue problems II", J. Math. Anal. Appl. 33 (1971) 425-432.

Alan L. Andrew, "Variational solution of some nonlinear eigenvalue problems I", J. Math. Anal. Appl. 32 (1970) 400-413. 

A. L. Andrew, "Convergence of approximate operator methods for eigenvectors", Bull. Austral. Math. Soc. 3 (1970) 199-205.

A. L. Andrew, "Application of the Ritz method to non-standard eigenvalue problems", J. Austral. Math. Soc. 10 (1969) 367-384.

A. L. Andrew, " Non-radial oscillations of massive stars by variational methods", Acad. Roy. Belg. Bull. Cl. Sci. 5me Ser. 54 (1968) 1046-1055

A. L. Andrew, " A note on the Ritz method with an application to overtone stellar pulsation theory", J. Austral. Math. Soc. 8 (1968) 275-286.

A. L. Andrew, "Higher modes of non-radial oscillations of stars by variational methods", Austral. J. Phys. 20 (1967) 363-368.

A. L. Andrew, "Two properties of integers", Math. Gazette 48 (1964), 285-287.