Work supported in part by the U. S. Army Scientific Research Office at The University of Texas, Austin, Texas, U.S.A.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Schatten, Robert, "A Theory of Cross-spaces," Annals of Mathematics Studies, No. 26, Princeton University Press, Princeton, 1950.
Robertson, A.P., and Wendy Robertson, "Topological Vector Spaces," Cambridge University Press, Cambridge, 1964.
Schaeffer, H. H., "Topological Vector Spaces," MacMillan Company, New York, 1966.
Gordon, W. J., "Blending-function methods of bivariate and multivariate interpolation and approximation," General Motors Research Laboratories, Report 834, October 1968.
Diliberto, S. P., and E. G. Straus, "On the approximation of a function of several variables by the sum of functions of fewer variables," Pacific J. Math. 1 (1951), 195–210.
Fulkerson, D. R., and P. Wolfe, "An algorithm for scaling matrices," SIAM Review 4 (1962), 142–146.
Bank, R., "An automatic scaling procedure for a d’Yakanov-Gunn iteration scheme," CNA Report 142, University of Texas at Austin, August 1978. To appear, Linear Algebra and Its Applications.
Bank, R., and D. J. Rose, "Marching algorithms for elliptic boundary value problems I: The constant coefficient case," SIAM J. on Numerical Analysis 14 (1977), 792–829.
Bank, R., "Marching algorithms for elliptic boundary value problems II: The variable coefficient case," SIAM J. on Numerical Analysis 14 (1977), 950–970.
Settari, A., and K. Aziz, "A generalization of the additive correction methods for the iterative solution of matrix equations," SIAM J. on Numerical Analysis 10 (1973), 506–521.
v. Golitschek, M., "An algorithm for scaling matrices and computing the minimum cycle mean in a digraph," preprint, August 1979, Institute for Applied Mathematics, University of Würzburg, Germany.
v. Golitschek, M., "Approximation of functions of two variables by the sum of two functions of one variable," preprint, August 1979, Institute for Applied Mathematics, University of Würzburg, Germany.
Rothblum, U. G., and H. Schneider, "Characterizations of optimal scalings of matrices," Report RS 2678 (1978), Yale University, New Haven.
Hammerlin, G., and L. L. Schumaker, "Procedures for kernel approximation and solution of Fredholm integral equations of the second kind," CNA Report 1 8, University of Texas at Austin, November 1977.
Atkinson, K., "A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind," SIAM, Philadelphia, 1976.
Phillips, G. M., J. H. McCabe, E. W. Cheney, "A mixed-norm bivariate approximation problem with applications to Lewanowicz operators," pp. 315–323 in "Multivariate Approximation," D.C. Handscomb, ed., Academic Press, New York, 1978. Also CNA Report 127, University of Texas at Austin, October 1977.
Krabs, W., "Optimierung und Approximation," B. G. Teubner, Stuttgart, 1975 (particularly Sec. 5.3).
Atlestam, B., and F. E. Sullivan, "Iteration with best approximation operators," Rev. Roumaine Math. Puras Appl. 21 (1976), 125–131. MR 53#6188.
Sullivan, F. E., "A generalization of best approximation operators," Ann. Mat. Pura Appl. 107 (1975), 245–261. MR 53#3564.
Aumann, G., "Uber Approximative Nomographie II," Bayer. Akad. Wiss. Math. Nat. Kl. S.B. 1959, 103–109. MR 22#6968.
Light, W. A., and E. W. Cheney, "On the approximation of a bivariate function by the sum of univariate functions," to appear, J. Approximation Theory. Also CNA Report 140, University of Texas at Austin, August 1978.
Kelley, C. T., "A note on the approximation of functions of several variables by sums of functions of one variable," Report 1873, Math. Research Center, Madison, Wisconsin, August 1978.
Dyn, R., "A straightforward generalization of Diliberto and Straus’ algorithm does not work," to appear, J. Approximation Theory. Report dated December 1978, Math. Research Center, Madison, Wisconsin.
Light, W. A., J. H. McCabe, G. M. Phillips, and E. W. Cheney, "The approximation of bivariate functions by sums of univariate ones using the L-1 metric," Report CNA 147, University of Texas at Austin, March 1979.
Golomb, M., "Approximation by functions of fewer variables," pp. 275–327 in "On Numerical Approximation," R. E. Langer, ed., University of Wisconsin Press, 1959.
Editor information
Rights and permissions
Copyright information
© 1980 Springer-Verlag
About this paper
Cite this paper
Cheney, E.W. (1980). Best approximation in tensor product spaces. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094161
Download citation
DOI: https://doi.org/10.1007/BFb0094161
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09740-2
Online ISBN: 978-3-540-38562-2
eBook Packages: Springer Book Archive