- Barcilon , V. 1990 . A two-dimensional inverse eigenvalue problem . Inverse Problems , 6 : 11 – 20 .
- Courant , R. and Hubert , D. 1953 . Methods of Mathematical Physics , Vol. 1 , New York, NY : Interscience .
- Dai , H. and Lancaster , P. 1997 . Newton's method for a generalized inverse eigenvalue problem . Numer. Linear Algebra Appl. , 4 (1) : 1 – 21 .
- El Badia , A. 1989 . On the uniqueness of a bi-dimensional inverse spectral problem . C. R. Acad. Sd. Paris Ser. I Math. , 308 (10) : 273 – 276 .
- Friedland , S. , Nocedal , J. and Overtoil , M. 1987 . The formulation and analysis of numerical methods for inverse eigenvalue problems . SIAM J. Numer. Anal. , 24 (3) : 634 – 667 .
- HaId , O.H. 1978 . The inverse Sturm-Liouville problem and the Rayleigh-Ritz method . Math. Camp. , 32 (143) : 687 – 705 .
- HaId , O.H. and McLaughlin , J.R. 1996 . Inverse Nodal Problems: Finding the Potential from Nodal Lines , Providence, RI : AMS Memoir .
- Knobel , R. and McLaughlin , J.R. 1994 . A reconstruction method for a two-dimensional inverse eigenvalue problem . Z. Angew. Math. Phys. , 45 : 794 – 826 .
- Lee , C.J. and McLaughlin , J.R. 1997 . “ Finding the density for a membrane from nodal lines ” . In Inverse Problems in Wave Propagation , Edited by: Chavent , G. , Papanicolaou , G. , Sacks , P. and Symes , W.W. 325 – 345 . New York, NY : Springer-Verlag .
- A.E.H. Love . 1944 . A Treatise on the Mathematical Theory of Elasticity Dover
- McCarthy , C.M. Recovery of a density from the eigenvalues for a nonhomogeneous membrane . Third International Conference on Inverse Problems in Engineering . Edited by: Woodbury , K.A. New York, NY : ASME .
- McCarthy , C.M. 2001 . The inverse eigenvalue problem for a weighted Heimholteequation . Applicable Analysis , 77 (1-2) : 77 – 96 .
- McLaughlin , J.R. Formulas for finding coeffiecients from nodes/nodal lines . Proceedings of the International Congress of Mathematicians . 1994 , Zurich, Switzerland. pp. 1494 – 1501 . Basel : Birkhäuser Verlag .
- McLaughlin , J.R. 2000 . “ Solving inverse problems with spectral data ” . In Surveys onSolution Methods for Inverse Problems , Edited by: Colton , D. , Engl , H.W. , Louis , A.K. , McLaughlin , J.R. and Rundell , W. 169 – 194 . Vienna : Springer-Verlag .
- McLaughlin , J.R. and Portnoy , A. 1998 . Perturbation expansions for eigenvaluesand eigenvectors for a rectangular membrane subject to a restorative force . Comm. Partial Differential Equations , 23 (1-2) : 243 – 285 .
- Nachman , A. , Sylvester , J. and Uhlmann , G. 1988 . An ç-dimensional Borg-Levinson theorem . Comm. Math. Phys. , 115 : 595 – 605 .
- Seidman , T. 1988 . An inverse eigenvalue problem with rotational symmetry . Inverse Problems , 4 : 1093 – 1115 .
- Stewart , G.W. 1973 . Introduction to Matrix Computations , San Diego, CA : Academic Press .
- Strang , O.S. and Fix , G.J. 1973 . An Analysis of the Finite Element Method , Englewood Cliffs, NJ : PrenticeHall .
- Titchmarsh , E.C. 1962 . Eigenfunction Expansions Associated with Second-OrderDifferential Equations , Vol. II , Oxford : Clarendon Press .
- Weinberger , H. Variational methods for eigenvalue approximation . CBMS-NSF Regional Conference Series in Applied Mathematics . Vol. 15 , Philadelphia, PA : SIAM .
- Choose new content alerts to be informed about new research of interest to you
- Easy remote access to your institution's subscriptions on any device, from any location
- Save your searches and schedule alerts to send you new results
- Export your search results into a .csv file to support your research