On least squares exponential sum approximation with positive coefficients

Evans, John W.; Gragg, William B.; LeVeque, Randall J.

doi:10.1090/S0025-5718-1980-0551298-6

On least squares exponential sum approximation with positive coefficients
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by John W. Evans, William B. Gragg and Randall J. LeVeque PDF

Math. Comp. 34 (1980), 203-211 Request permission

Abstract:

An algorithm is given for finding optimal least squares exponential sum approximations to sampled data subject to the constraint that the coefficients appearing in the exponential sum are positive. The algorithm employs the divided differences of exponentials to overcome certain problems of ill-conditioning and is suitable for data sampled at noninteger times.

References

D. Braess, Approximation mit Exponentialsummen, Computing (Arch. Elektron. Rechnen) 2 (1967), 309–321 (German, with English summary). MR 233120, DOI 10.1007/bf02235808
Dietrich Braess, Chebyshev approximation by exponentials on finite subsets, Math. Comp. 27 (1973), 327–331. MR 330854, DOI 10.1090/S0025-5718-1973-0330854-0
David G. Cantor and John W. Evans, On approximation by positive sums of powers, SIAM J. Appl. Math. 18 (1970), 380–388. MR 277090, DOI 10.1137/0118032
S. D. Conte, Elementary numerical analysis: An algorithmic approach, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1965. MR 0202267
C. B. Dunham, Nonlinear mean-square approximation of finite sets, SIAM J. Numer. Anal. 12 (1975), 105–110. MR 361565, DOI 10.1137/0712010
Charles L. Lawson and Richard J. Hanson, Solving least squares problems, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. MR 0366019
Cleve Moler and Charles Van Loan, Nineteen dubious ways to compute the exponential of a matrix, SIAM Rev. 20 (1978), no. 4, 801–836. MR 508383, DOI 10.1137/1020098
G. Opitz, Steigungsmatrizen, Z. Angew. Math. Mech. 44 (1964), T52–T54 (German). MR 185806, DOI 10.1002/zamm.19640441321
Robert C. Ward, Numerical computation of the matrix exponential with accuracy estimate, SIAM J. Numer. Anal. 14 (1977), no. 4, 600–610. MR 445806, DOI 10.1137/0714039
W. J. Wiscombe and J. W. Evans, Exponential-sum fitting of radiative transmission functions, J. Comput. Phys. 24 (1977), no. 4, 416–444. MR 494842, DOI 10.1016/0021-9991(77)90031-6