Talk by James Nagy, Emory University

SVD Approximations for Large Scale Inverse Problems

Abstract

Beginning with his 1982 PhD thesis, SVD: Theory and Applications [1], Per Christian Hansen has written numerous important papers that analyze and promote the use of the singular value decomposition for ill-posed inverse problems. In particular, he makes use of the SVD in his most highly cited publications [2, 3, 4, 5], which currently have more than 10000 citations. Moreover, Per Christian has written at least 14 other journal articles (with another 1800+ citations) that have SVD directly in the title. In this talk we provide a brief historical review of some of this early influential work by Per Christian, and use it as motiviation to develop results for a new SVD approximation for large scale inverse problems.

References

[1] P. C. Hansen. SVD – Theory and Applications. PhD Thesis, Danmarks Tekniske Højskole, Numerisk Institut, 1982.
[2] P. C. Hansen. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Review, 34:561–580, 1992.
[3] P. C. Hansen. Regularization tools: A Matlab package for the analysis and solution of discrete ill-posed problems. Numerical Algorithms, 6:1–35, 1994.
[4] P. C. Hansen. Rank-deficient and discrete ill-posed problems. SIAM, Philadelphia, PA, 1997.
[5] P. C. Hansen and D. P. O’Leary. The use of the L-curve in the regulariza- tion of discrete ill-posed problems. SIAM J. Sci. Comput., 14:1487–1503, 1993.