The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
A Numerical Method for Solving Fredholm Integral Equations of the First Kind Using Singular Values
Abstract
The integral equation in question is approximated by simple numerical quadrature formulas plus collocation. Each row of the resulting matrix equation for the unknown function values is weighted by the reciprocal of the standard deviation of the known function. A singular value decomposition is used to obtain a solution for the resulting linear system. By avoiding the use of the smallest singular values, an approximate solution is calculated which frequently solves the problem “close enough” and removes a great deal of the oscillations in the solution which are inherently present due to the ill-posed nature of the problem. Test cases and computational results are presented.
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Citations
Cites
Singular value decomposition and least squares solutions
Golub, G. H., & Reinsch, C. (1970) · Numerische Mathematik · doi:10.1007/bf02163027 · Cited by 2,929
Algorithm 358: singular value decomposition of a complex matrix [F1, 4, 5]
Businger, P. A., & Golub, G. H. (1969) · Communications of the ACM · doi:10.1145/363235.363249 · Cited by 143
Cited by
Spectrum estimation and harmonic analysis
Thomson, D. J. (1982) · Proceedings of the IEEE · doi:10.1109/proc.1982.12433 · Cited by 4,418
Maximum entropy analysis of oversampled data problems
Bryan, R. K. (1990) · European Biophysics Journal · doi:10.1007/bf02427376 · Cited by 335
Metadata
- Authors
- Hanson, R. J.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1971-09
- Volume
- 8
- Issue
- 3
- Pages
- 616-622
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W1977120413
- Cited by
- 200
- References
- 2
- FWCI
- 3.75
- Type
- journal article
- Language
- en
- Open access
- closed
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- Hanson, R. J. (1971). A Numerical Method for Solving Fredholm Integral Equations of the First Kind Using Singular Values. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0708058
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