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 Michael Rauth - GEOPHYSICS and COMPUTING
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My BibTeX Database

This is the list of references that I used in the time I was doing research for my thesis.


Updated on Mon Jul 27 8:14:59 1998

[1]
J. Abaffy and E Spedicato. ABS Projection Algorithms: Mathematical techniques for Linear and Nonlinear Equations. Halsted Press, 1989.

[2]
H. Akima. Algorithm 526; bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Trans. Math. Software, 4:160-164, 1978.

[3]
H. Akima. A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Trans. Math. Software, 4(2):148-159, 1978.

[4]
G. Ammar and W. Gragg. Superfast solution of real positive definite Toeplitz systems. SIAM J. Matrix Anal. Appl., 9:61-76, 1988.

[5]
I. J. Anderson and J. C. Mason. Surface fitting by exploiting data distribution. preprint, 1994.

[6]
O. Axelsson and G. Lagendijk. On the rate of convergence of the preconditioned conjugate gradient algorithm. Numer. Math., 48:499-523, 1986.

[7]
L. Bacchelli Montefusco and G. Casciola. c^1 surface interpolation. ACM Trans. Math. Software, 15:365-374, 1989.

[8]
Y. Baram and M. Margalit. Surface fitting by pseudo-potential functions. IEEE Trans. Geosc. and Remote Sens., GE-52(5):455-460, 1984.

[9]
Y. Baram. On two-dimensional data representation by radial base functions. IEEE Trans. Acoust. Speech Sig. Proc., 32, 1984.

[10]
W. Baranov. Potential fields and their transformations in applied geophysics. Number 6 in Geoexploration Monographs. Gebrüder Borntraeger, Berlin - Stuttgart, 1975.

[11]
I. Barrodale, R. Kuwahara, R. Poeckert, and D. Skea. Processing side-scan sonar images using thin plate splines. Presented at the NATO Advanced Research Workshop on Algorithms for Approximation, Oxford, July 1992.

[12]
B.J.C. Baxter. The interpolation theory of radial basis functions. PhD thesis, University of Cambridge, 1992.

[13]
J. Besag, J. York, and A. Mollie. Bayesian image restoration with two applications in spatial statistics. Ann. Inst. Statist. Math., 43:1-59, 1991.

[14]
G. Beylkin. On the fast Fourier transform of functions with singularities. Appl. Comp. Harm. Anal., 2(4):363-381, 1995.

[15]
B.K Bhattacharyya and K.C Chan. Reduction of magnetic and gravity data on an arbitrary surface acquired in a region of high topographic relief. Geophysics, 42(7):1411-1430, 1977.

[16]
B.K. Bhattacharyya and Lei-Kuang Leu. Spectral analysis of gravity and magnetic anomalies due to rectangular bodies. Geophysics, 42(1):41-50, February 1977.

[17]
B.K. Bhattacharyya. Two-dimensional harmonic analysis as a tool for magnetic interpretation. Geophysics, 30(5):829-857, October 1965.

[18]
B.K. Bhattacharyya. Continuous spectrum of the total-magnetic-field anomaly due to a rectangular prismatic body. Geophysics, 31(1):97-121, 1966.

[19]
B.K. Bhattacharyya. Bicubic spline interpolation as a method for treatment of potential field data. Geophysics, 34(3):402-423, June 1969.

[20]
R.R. Bitmead and B.D. Anderson. Asymptotically fast solution of Toeplitz and related systems of linear equations. Linear Algebra Appl., 34:103-117, 1980.

[21]
A. Björck. Numerical Methods for Least Squares Problem. SIAM, 1996.

[22]
R.J. Blakely. Potential theory in gravity and magnetic applications. Cambridge University Press, 1995.

[23]
P.D. Bourke. A contouring subroutine. Byte, 12:143-150, 1987.

[24]
I.C. Briggs. Machine contouring using minimum curvature. Geophysics, 39(1):39-48, 1974.

[25]
M.D. Buhmann and N. Dyn. Error estimates for multiquadric interpolation. In P. J. Laurent, LeMéhauté, and Schuhmaker L. L., editors, Curves and Surface. Academic Press, 1991.

[26]
M.D. Buhmann. Multivariable interpolation with radial basis functions. Comput. Math. Appl., preprint, 1990.

[27]
J.R. Bunch. Stability of methods for solving Toeplitz systems of equations. SIAM J. Sci. Statist. Comp., 6:349-364, 1985.

[28]
P. L. Butzer and G. Hinsen. Two-dimensional nonuniform sampling expansions - an iterative approach. I, II. Appl. Anal. 32, pages 53-68 and 69-85, 1989.

[29]
P. L. Butzer, W. Splettstösser, and R. L. Stens. The sampling theorem and linear prediction in signal analysis. Jahresbericht der DMV 90, pages 1-70, 1988.

[30]
M. Carbonell, R. Oliver, and J.L. Ballester. Power spectra of gapped time series: a comparison of several methods. Astronom. and Astrophys., 264:350-360, 1992.

[31]
D.W. Caress and R.L. Parker. Spectral interpolation and downward continuation of marine magnetic anomaly data. J. Geophys. Res., 94(B12):17393-17407, Dec 1989.

[32]
C. Cenker, H.G. Feichtinger, M. Mayer, H. Steier, and T. Strohmer. New variants of the pocs method using affine subspaces of finite codimension, with applications to irregular sampling. In Proc.Conf. SPIE 92 Boston, pages 299-310, 1992.

[33]
R.H. Chan and G. Strang. Toeplitz equations by conjugate gradients with circulant preconditioner. SIAM J. Sci. Statist. Comp., 10:104-119, 1989.

[34]
T. Chan. An optimal circulant preconditioner for Toeplitz systems. SIAM J. Sci. Statist. Comp., 9:766-771, 1989.

[35]
D. Shi Chen and J.P. Allebach. Analysis of error in reconstruction of two-dimensional signals from irregularly spaced samples. IEEE Trans. Acoust. Speech Sig. Proc., ASSP-35(2), February 1987.

[36]
B. Cianicara and H. Marcak. Interpretation of gravitiy anomalies by means of local power spectra. Geophys. Prosp., 24:273-286, 1976.

[37]
L. Cordell and V.J.S Grauch. Reconciliation of the discrete and integral Fourier transforms. Geophysics, 47(2):237-243, 1982.

[38]
L. Cordell. A scattered equivalent-source method for interpolation and gridding of potential field data in three dimensions. Geophysics, 57(4):629-636, 1992.

[39]
N. A. Cressie. Statistics for spatial data. Wiley, 1993.

[40]
C.N.G. Dampney. The equivalent source technique. Geophysics, 34(1):39-53, 1969.

[41]
P.J. Davis. Circulant Matrices. John Wiley, 1979.

[42]
W.C Dean. Frequency analysis for gravity and magnetic interpretation. Geophysics, 23:97-127, 1958.

[43]
T.J. Deeming. Fourier analysis with unequaly spaced data. Astrophys. Space Sci., 36:137-158, 1975.

[44]
C.V. Deutsch and A.G. Journel. GSLIB - Geostatistical software library and user's guide. Oxford University Press, 1992.

[45]
J. Duchon. Splines minimizing rotation-invariant seminorms in Sobolev spaces. In W. Schempp and K. Zeller, editors, Constructive theory of functions of several variables, volume 571 of Lecture notes in mathematics, pages 85-100. Springer Verlag, Berlin, 1977.

[46]
A.J.W. Duijndam and M.A. Schonewille. Nonuniform fast Fourier transform. In 67th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, volume 97, 1997.

[47]
A. Duijndam, M. Schonewille, and C.O.H. Hindriks. Reconstruction of band-limited data irregularly sampled along one spatial direction. preprint, 1997.

[48]
A. Dutt and V. Rokhlin. Fast Fourier transformation for nonequispaced data. SIAM J. Sci. Comp., 14(6):1368-1393, November 1993.

[49]
A. Dutt and V. Rokhlin. Fast Fourier transforms for nonequispaced data II. Appl. Comp. Harm. Anal., 2(1):85-10, 1995.

[50]
N. Dyn, D. Levin, and S. Rippa. Numerical procedures for surface fitting of scattered data by radial functions. SIAM J. Sci. Statist. Comp., 7:639-659, 1986.

[51]
N. Dyn, I.R.H. Jackson, D. Levin, and A. Ron. On multivariate approximation by integer translates of a basis function. IEEE Trans. Systems Man Cybernet., 78:95-130, 1992.

[52]
N Dyn. Interpolation of scattered data by radial functions. In C.K. Chui, L.L. Schuhmaker, and F.I. Uteras, editors, Topics in Multivariate Approximation. Academic Pres, 1987.

[53]
C.G. Fahlman and T.J. Ulrych. A new method for estimating the power spectrum of gapped data. Monthly Notices Roy. Astronom. Soc., 199:53-65, 1982.

[54]
Gerald E. Farin. Curves and Surfaces for Computer Aided Geometric Design : A Practical Guide. Academic Press, Boston, 2nd edition, 1990.

[55]
H.G. Feichtinger and K. Gröchenig. Multidimensional irregular sampling of band-limited functions in l^p-spaces. Conf. Oberwolfach Feb. 1989, pages 135-142, 1989.

[56]
H.G. Feichtinger and K. Gröchenig. Irregular sampling theorems and series expansions of band-limited functions. J. Math. Anal. Appl., 167:530-556, 1992.

[57]
H.G. Feichtinger and K. Gröchenig. Iterative reconstruction of multivariate band-limited functions from irregular sampling values. SIAM J. Math. Anal., 231:244-261, 1992.

[58]
H.G. Feichtinger and K. Gröchenig. Error analysis in regular and irregular sampling theory. Appl. Anal., 50:167-189, 1993.

[59]
H.G. Feichtinger and K.H. Gröchenig. Theory and practice of irregular sampling. In J. Benedetto and M. Frazier, editors, Wavelets: Mathematics and Applications, pages 305-363. CRC Press, 1994.

[60]
H.G. Feichtinger and T. Strohmer. Irsatol -- irregular sampling of band-limited signals toolbox. In K. Dette, D. Haupt, and C. Polze, editors, Conf. Computers for Teaching, Berlin, pages 277-284, 1992.

[61]
H.G. Feichtinger and T. Strohmer. Fast iterative reconstruction of band-limited images from irregular sampling values. In D. Chetverikov and W.G. Kropatsch, editors, Proc. Conf. on Computer Analysis of Images and Patterns, pages 82-91, Budapest, 1993.

[62]
H.G. Feichtinger and T. Strohmer. Recovery of missing segments and lines in images. Optical Engineering: special issue on ``Digital Image Recovery and Synthesis'', 33(10):3283-3289, 1994.

[63]
H.G. Feichtinger, K. Gröchenig, and M. Hermann. Iterative methods in irregular sampling theory. In Numerical Results. 7. Aachener Symposium für Signaltheorie. ASST 1990, Aachen, Informatik Fachber. 253, pages 160-166. Springer, 1990.

[64]
H.G. Feichtinger, C. Cenker, and M. Herrmann. Iterative algorithms in irregular sampling: A first comparison of methods. In Conf. ICCCP`91, March 1991, Phoenix, USA, pages 483-489, 1991.

[65]
H.G. Feichtinger, C. Cenker, and H. Steier. Fast iterative and non-iterative reconstruction methods in irregular sampling. Conf. ICASSP`91, May, Toronto, pages 1773-1776, 1991.

[66]
H.G. Feichtinger, K. Gröchenig, and T. Strohmer. Efficient numerical methods in non-uniform sampling theory. Numer. Math., 69:423-440, 1995.

[67]
H.G. Feichtinger. New mathematical tools in digital signal processing. In GMÖOR Proceedings. Conf. Oper. Res., Vienna, Haid Verlag, 1990.

[68]
H.G. Feichtinger. Pseudo-inverse matrix methods for signal reconstruction from partial data. In SPIE-Conf., Visual Comm. and Image Proc., Boston, pages 766-772, 1991. Int.Soc.Opt.Eng.

[69]
H.G. Feichtinger. Reconstruction of band-limited signals from irregular samples, a short summary, 1991. ÖCG.

[70]
H.G. Feichtinger. personal communication, 1998.

[71]
S. Ferraz-Mello. Estimation of periods from unequally spaced observations. Astronom. J., 86:619-624, 1981.

[72]
M.A. Fiddy. The role of analyticity in image recovery. In H. Stark, editor, Image Recovery: Theory and Application, pages 499-530. Academic Press, 1987.

[73]
P. W. Fieguth, C. K. William, A. S. Willsky, and C. Wunsch. Multiresolution optimal interpolation and statistical analysis of Topex/Poseidon satellite altimetry. preprint, 1994.

[74]
M. S. Floater and A. Iske. Thinning algorithms for scattered data interpolation. preprint.

[75]
M. S. Floater and A. Iske. Multistep scattered data interpolation using compactly supported radial basis functions. J. Comput. Appl. Math., 73(5):65-78, 1996.

[76]
M. S. Floater and A. Iske. Thinning, inserting, and swapping scattered data. In A. Le Méhauté, C. Rabut, and L. L. Schuhmaker, editors, Proceedings of Chamonix, Nashvill, TN, 1996. Vanderbilt University Press.

[77]
T.A. Foley and H. Hagen. Advances in scattered data interpolation. Surv. Math. Ind., 4:71-84, 1994.

[78]
James D. Foley, Andries van Dam, Feiner, and Hughes. Computer Graphics : Principles And Practice. Addison-Wesley Systems Programming Series. Addison-Wesley, Reading, Mass., 2nd edition, 1990.

[79]
T.A. Foley. Three-stage interpolation to scattered data. Rocky Mountain J. Math., 14(1):141-149, 1984.

[80]
F. Fontanella, K. Jetter, and P.J. Laurent, editors. Advanced Topics in Multivariate Approximation. Number 8 in Series in Approximations and Decompositions. World Scientific, Singapore, 1996.

[81]
C. Ford and D.M. Etter. Wavelet-based interpolation method for nonuniformly sampled data fields. In Proceedings of the International Symposium on Optical Science, Engineering, and Instrumentation, Aug 1996. Denver, U.S.A.

[82]
G. Foster. The CLEANEST Fourier spectrum. Astronom. J., 109(4):1889-1902, Apr 1995.

[83]
G. Foster. Time series analysis by projection. i. statistical properties of Fourier analysis. Astronom. J., 111(1):541-554, Jan 1996.

[84]
G. Foster. Time series analysis by projection. ii. tensor methods for time series analysis. Astronom. J., 111(1):555-566, Jan 1996.

[85]
G. Foster. Wavelets for period analysis of unevenly sampled time series. Astronom. J., 112(4):1709-1729, Oct 1996.

[86]
R. Franke and G. Nielson. Smooth interpolation of large sets of scattered data. Internat. J. Numer. Methods Engrg., 15:1691-1704, 1980.

[87]
R. Franke. Scattered data interpolation: test of some methods. Math. Comp., 33(157):181-200, 1982.

[88]
D. Fuller. Two-dimensional frequency analysis and design of grid operators. Mining Geophys., 2:658-708, 1967.

[89]
D. Geman. Random Fields and Inverse Problems in Imaging, volume 1427 of Lecture Notes in Mathematics. Springer-Verlag, 1990.

[90]
D. Gibert and A Galdeano. A computer program to perform transformations of gravimetric and aeromagnetic surveys. Comput. Geosci., 11:553-588, 1985.

[91]
G.H. Golub and C.F. van Loan. Matrix Computations, third ed.. Johns Hopkins, London, Baltimore, 1996.

[92]
G. Goodsell. On finding p-th nearest neighbours of scattered points in two dimensions for samll p. Numerical analysis reports, University of Cambridge, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, England, Jan 1997.

[93]
H. Granser, P. Steinhauser, D. Ruess, and B. Meurers. Beiträge zur Erkundung der Untergrundstrukturen der Neusiedlersee-Region mit gravimetrischen und magnetischen Methoden. Mitt. Österr. Geolog. Ges., 84:223-238, 1991.

[94]
William Eric Leifur Grimson. From Images to Surfaces : A Computational Study of the Human Early Visual System. Artificial intelligence. MIT Press, Cambridge, Mass., 1981.

[95]
K. Gröchenig. A new approach to irregular sampling of band-limited functions. In J.S. Byrnes and J.L. Byrnes, editors, Recent Advances in Fourier Analysis and Its Applications', Series C, volume 315, pages 251-260. Kluwer Acad. Publ., 1990.

[96]
K. Gröchenig. Describing functions: atomic decompositions versus frames. Monatsh. Math., 112:1-41, 1991.

[97]
K. Gröchenig. Efficient algorithms in irregular sampling of band-limmited functions. In Proceedings of the 10^rm th annual ICCCP, March `91, Scottsdale, Arizona, USA, pages 490-495. IEEE Computer Society Press, 1991.

[98]
K. Gröchenig. Reconstruction algorithms in irregular sampling. Math. Comp., 59:181-194, 1992.

[99]
K. Gröchenig. Acceleration of the frame algorithm. IEEE Trans. Signal Proc., 41(12):3331-3340, 1993.

[100]
K. Gröchenig. A discrete theory of irregular sampling. Linear Algebra Appl., 193:129-150, 1993.

[101]
K. Gröchenig. Irregular sampling of wavelet and short time Fourier transform. Constr. Approx., 9:283-297, 1993.

[102]
K. Gröchenig. Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type, 1994. Preprint.

[103]
K. Gröchenig. Finite and infinite-dimensional models of non-uniform sampling. In Proc. SampTA'97, Aveiro, Portugal, pages 285-290, Jun 1997.

[104]
K. Gröchenig. personal communication, 1998.

[105]
L.J. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. ACM Trans. Graphics, 4:74-123, 1985.

[106]
P.J. Gunn. Application of Wiener filters to transformations of gravity and magnetic fields. Geophys. Prosp., 20:860-871, 1972.

[107]
P.J. Gunn. Linear transformations of gravity and magnetic field. Geophys. Prosp., 23:300-312, 1975.

[108]
K. Guo and X. Sun. Scattered data interpolation by linear combinations of translates of conditionally positive definite functions. Numer. Funct. Anal. Optim., 12:137-152, 1991.

[109]
R. Gutdeutsch. Anwendungen der Potentialtheorie auf geophysikalische Felder. Springer-Verlag Berlin, 1986.

[110]
L.A. Hageman and D.M. Young. Applied Iterative Methods. Academic Press, 1981.

[111]
H. Hagen and T. Schreiber. Scattered Data Algorithmen zur Umweltdatenvisualisierung. In R. Denzu, H. Hagen, and K.H. Kutschke, editors, Visualisierung von Umweltdaten, volume 274 of Informatik Fachberichte, pages 22-28. Springer, 1991.

[112]
W. F. Hanna. Some historical notes on early magnetic surveying in the U.S. Geological Survey. In Hanna W. F., editor, Geologic application of modern aeromagnetic surveys, number 1924 in U.S. Geological Survey Bulletin, pages 63-73. U.S. Geological Survey, Denver, CO, 1990.

[113]
R.O. Hansen and Y. Miyazaki. Continuation of potential fields between arbitrary surfaces. Geophysics, 49(6):787-797, Jun 1984.

[114]
R. O. Hansen and X. Wang. Simplified frequency-domain expressions for potential fields of arbitrary three-dimensional bodies. Geophysics, 53(3):365-374, March 1988.

[115]
R.O. Hansen. Interpretive gridding by anisotropic kriging. Geophysics, 58(10):1491-1497, 1993.

[116]
R.L. Hardy and S.A. Nelson. A multiquadratic-biharmonic representation of disturbing potentials. Geophys. Res. Letters, 13(1):18-21, 1986.

[117]
R.L. Hardy. Multiquadratic equations of topography and other irregular surface. J. Geophys. Res., 76(8):1905-1915, 1971.

[118]
R.L. Hardy. Surface fitting with biharmonic and harmonic models. In Proceedings of the NASA workshop on surface fitting, pages 136-146, College Station, Texas, 1982. Texas A & M Univeristy.

[119]
M.H. Hayes. The unique reconstruction of multidimensional sequences from Fourier transform magnitude or phase. In H. Stark, editor, Image Recovery: Theory and application, pages 195-230. Acad. Press, 1987.

[120]
A. Heck, J. Manfroid, and G. Mers. On period determination method. Astrophys. Space Sci., 59:63-72, 1985.

[121]
R.G. Henderson and L. Cordell. Reduction of unevenly spaced potential field data to a horizontal plane by means of finite harmonic series. Geophysics, 36(5):856-866, Oct 1971.

[122]
J. R. Higgins. Five short stories about the cardinal series. Bull. Amer. Math. Soc. (N.S.), 12:45-89, 1985.

[123]
J.R. Higgins. Sampling Theory in Fourier and Signal Analysis: Foundations. Oxford University Press, 1996.

[124]
J.A. Högbom. Aperture synthesis with a non-regular distribution of interferometer baselines. Astrophys. Space Sci., 15:417-426, 1986.

[125]
J.H. Horne and S.L. Baliunas. A prescription for period analysis of unevenly sampled time series. Astrophys. J., 302:757-763, 1986.

[126]
T. Huckle. Symmetric gaussian elimination for cauchy-type matrices with application to positive definite Toeplitz matrices. submitted to Numerische Mathematik.

[127]
A.J. Jerri. The Shannon sampling theorem - its various extensions and applications, a tutorial review. Proc. IEEE, 65:1565-1596, 1977.

[128]
A. G. Journel and Ch. J. Huijbregts. Mining geostatistics. Academic Press, London, 1978.

[129]
E.R. Kanasewich and R.G. Agarwal. Analysis of combined gravity and magnetic fields in wave number domain. J. Geophys. Res., 75(29):5702-5712, October 1970.

[130]
D.E. Knuth, L.J. Guibas, and M. Sharir. Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica, 7(4):381-413, 1992.

[131]
G. Kraiger. Influence of the curvature parameter on least-squares prediction. Manuscripta Geodaet., 13:164-171, 1988.

[132]
D.G. Krige. A statistical approach to some mine valuation and allied problems on the Witwatersrand. Master's thesis, University of the Witwatersrand, 1951.

[133]
T.K. Ku and C.J. Kuo. On the spectrum of a family of preconditioned block Toeplitz matrices. Tech.Rep., USC, Signal and Image Proc. Inst., 164, 1990.

[134]
T.K. Ku and C.J. Kuo. Design and analysis of Toeplitz preconditioners. IEEE Trans. SSP, 40:129-141, 1992.

[135]
J.R. Kuhn. Recovering spectral information from unevenly sampled data: two machine-efficient solutions. Astronom. J., 87:196-202, 1982.

[136]
B. Lahmeyer. Gravity field continuation of irregularly spaced data using least squares collocation. Geophys. J., 95:123-134, 1988.

[137]
D. T. Lee and B. J. Schlachter. Two algorithms for constructing a Delaunay triangulation. Internat. J. Comp. Informat. Sci., 9(3):219-242, 1980.

[138]
N.R. Lomb. Least-squares frequency analysis of unequally spaced data. Astrophys. Space Sci., 39:447-462, 1976.

[139]
A. E. H. Love. A treatise on the mathematical theory of elasticity. Dover Publ. Inc., 4 edition, 1927.

[140]
W.R. Madych and S.A. Nelson. Multivariate interpolation and conditionally positive definte functions. Approx. Theory Appl., 4:77-89, 1988.

[141]
W.R. Madych and S.A. Nelson. Multivariate interpolation and conditionally positive definte functions ii. Math. Comp., 54:211-230, 1990.

[142]
R.J. Marks. Introduction to Shannon Sampling and Interpolation Theory. Springer-Verlag, New York, 1991. Engineering Library 511.42 M342i 1991.

[143]
Farokh A. Marvasti. A Unified Approach to Zero-Crossings and Nonuniform Sampling of Single and Multidimensional Signals and Systems. Nonuniform Pub., 1987.

[144]
G. Matheron. The theory of regionalized variables and its applications. Cahier Centre Morphologie Math., 5:211pp., 1971.

[145]
J. Meinguet. Surface spline interpolation: basic theory and computational aspects. In S.P. et al. Singh, editor, Approximation theory and spline functions, pages 127-142. D.Reidel Publishing company, 1984.

[146]
J. Meinguet. Fondements mathematiques de l'interpolation par surfaces-spline. Séminar mathématique, rapport n^o 76, Universite Catholique de Louvain, Institut de Mathematique Pure et Appliquee, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgique, October 1985.

[147]
D. Menemenlis, P. Fieguth, C. Wunsch, and A. Willsky. A fast optimal interpolation algorithm for mapping hydrographic and other oceanographic data. preprint, 1996.

[148]
C.A. Micchelli. Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr. Approx., 2:11-22, 1986.

[149]
H. Militzer and F. Weber. Gravimetrie und Magnetik, volume 1 of Angewandte Geophysik. Spriger-Verlag Wien New York, 1989.

[150]
D.P. Mitchell. Generating antialiased images at low sampling densities. In Computer Graphics (SIGGRAPH '87 Proceedings), volume 21-4, pages 65-72, July 1987.

[151]
H. Moritz. Least-squares collocation. Rev. Geophys. Space Phys., 16:27-36, 1978.

[152]
P. S. Naidu and M. P. Mathew. Fast reduction of potential fields measured over an uneven surface to a plane surface. IEEE Trans. Geosc. and Remote Sens., 32(3):508-512, May 1994.

[153]
F.J. Narcowich and J.D. Ward. Norm estimates for the inverses of a general class of scattered data interpolation matrices. Texas A & M University, preprint, 1991.

[154]
F.J. Narcowich and J.D. Ward. Norm estimates of scattered data matrices with completely monotonic radial functions. Texas A & M University, preprint, 1991.

[155]
F.J. Narcowich and J.D. Ward. Norms of inverses and condition numbers for matrices associated with scattered data. J. Approx. Theory, 64:69-94, 1991.

[156]
R.A. Olea. Optimal contour mapping using universial kriging. J. Geophys. Res., 79(5):695-702, Feb 1974.

[157]
J.D. O'Sullivan. A fast sinc function gridding algorithm for Fourier inversion in computer tomography. IEEE Trans. Medical Imag., 4:200-207, 1985.

[158]
A. Papoulis. Signal analysis. McGraw-Hill, New York, 1977.

[159]
B. Pedersen. Wavenumber domain expressions for potential fields from arbitrary 2-, 21/2-, and 3-dimensional bodies. Geophysics, 43(3):626-630, April 1978.

[160]
M.J.D. Powell. Radial basis functions for multivariate interpolation: a review. In D.F. Griffiths and G.A. Watson, editors, Numerical Analysis, pages 223-241. Longman Scientific & Technical (Harlow), 1987.

[161]
M.J.D. Powell. Tabulation of thin plate splines on a very fine two- dimensional grid. In D. Braess and L. L. Schuhmaker, editors, Numerical Methods in Approximation Theory, pages 221-244. Birkhäuser Verlag, 1991.

[162]
M.J.D. Powell. Truncated Laurent expansions for the fast evaluation of thin plate splines. Numerical analysis reports, University of Cambridge, Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, England, December 1992.

[163]
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