%ONeill1966a \rhl{O} \refB O'Neill, B.; Elementary Differential Geometry; Academic Press (New York); 1966; %OberleOpfer1994 % larry \rhl{O} \refP Oberle, H. J., Opfer, G.; Splines with prescribed modified moments; \ChamonixIIa; 343--352; %OberleOpfer1998 % carl 12mar97 24mar99 \rhl{O} \refJ Oberle, H.-J., Opfer, G.; Non-negative splines, in particular of degree five; % Mathematik, Universit\"at Hamburg: 1996: \NM; 79; 1998; 427--450; % constraints %Oberst1995a % author 5dec96 \rhl{O} \refJ Oberst, Ulrich; Variations of the fundamental principle for linear systems of partial differential and difference equations; AAECC; 6; 1995; 211--243; %Oberst1996a % carl 5dec96 \rhl{O} \refJ Oberst, Ulrich; Finite dimensional systems of partial differential or difference equations; \AiAM; 17(3); 1996; 337--356; %OdyniecLewicki1990 % author 04mar10 \rhl{} \refB Odyniec, Wl., Lewicki, G.; Minimal projections in Banach spaces; Lecture Notes in Math., vol.~1449, Springer-Verlag (Berlin); 1990; % minimal projector %Ohair1978 \rhl{O} \refR O'Hair, K.; CONTx: contours from irregular data points; Lawrence Livermore; 1978; %Okada1969 % larry \rhl{O} \refJ Okada, Y.; A numerical experiment on the fairing free-form curves; Info.\ Process.\ in Japan; 9; 1969; 69--74; %OkinoKakazuKuboHashimotoShiroma1982 % larry \rhl{O} \refJ Okino, N., Kakazu, Y., Kubo, H., Hashimoto, N., Shiroma, Y.; Advanced $3D$ shape description methods in TIPS--1; Computers in Industry; 3; 1982; 93--104; %Olea1974 \rhl{O} \refJ Olea, R. A.; Optimal contour mapping using universal Kriging; J. Geophysical Res.; 78; 1974; 695--702; %Olea1975 \rhl{O} \refR Olea, R. A.; Optimum mapping techniques using regionalized variable theory; Series on Spatial Analysis \#2, Kansas Geological Survey; 1975; %Olea1977 \rhl{O} \refR Olea, R. A.; Measuring spatial dependence with semivariograms; Series on Spatial Analysis \#3, Kansas Geological Survey; 1977; %Olmsted1986a % shayne 14sep95 \rhl{O} \refJ Olmsted, C.; Two formulas for the general multivariate polynomial which interpolates a regular grid on a simplex; \MC; 47; 1986; 275--284; % see earlier proof of the result in Silvester70 (which is not quoted!) %OlsenAndries1976 \rhl{O} \refR Olsen, J. J., Andries, R. A.; Surface fitting to cambered airfoils; Air Force Dynamics Lab; 1976; %Olver2006 % carl 04mar10 \rhl{} \refJ Olver, Peter; On multivariate interpolation; Stud.\ Appl.\ Math.; 116(2); 2006; 201--240; %Omohundro1990a % . \rhl{O} \refR Omohundro, Stephen M.; The Delaunay triangulation and function learning; TR-90-001, International Computer Science Institute; 1990; % proves that, when interpolating at the points of mesh to a function % whose second derivatives are bounded by a certain constant, then the % best possible error is to be had by the piecewise linear interpolant % on a Delaunay triangulation of the mesh. %Omohundro1990b % . \rhl{O} \refJ Omohundro, Stephen M.; Geometric learning algorithms; Physica D; 42; 1990; 307--321; %Omwa1989 \rhl{O} \refR Omwa, A. A.; Reconstruction of a closed three-dimensional body by set-valued interpolation; xx; xx; %Ong1994 % ming Lai-Schumaker book \rhl{Ong94} \refJ Ong, M. E.; Uniform refinement of a tetrahedron; \SJSC; 15; 1994; 1134--1144; %OngCJWongYSLohHTHongXG1996 % . 08apr04 \rhl{} \refJ Ong, C. J., Wong, Y. S., Loh, H. T., Hong, X. G.; An optimization approach for biarc curve-fitting of B-spline curves; \CAD; 28(12); 1996; 951--959; %Operstein1995a % shayne 14sep95 \rhl{O} \refJ Operstein, V. A.; A characterisation of smoothness in terms of approximation by algebraic polynomials in $L_p$; \JAT; 81; 1995; 13--22; % approximation by (algebraic) polynomials measured in $L_p$-moduli of % smoothness %Opfer1989 % larry \rhl{O} \refP Opfer, G.; Necessary optimality conditions for splines under constraints; \TexasVI; 511--514; %OpferOberle1988a % carl \rhl{O} \refJ Opfer, Gerhard, Oberle, Hans Joachim; The derivation of cubic splines with obstacles by methods of optimization and optimal control; \NM; 52; 1988; 17--31; %OpferPuri1981 % sonya \rhl{O} \refJ Opfer, G., Puri, M. L.; Complex planar splines; \JAT; 31; 1981; 383--402; %OpferSchober1982 \rhl{O} \refJ Opfer, G., Schober, G.; On convergence and quasiregularity of interpolating complex planar splines; \MZ; 180; 1982; 469--481; %OpicKufner1990a % shayne 05feb96 \rhl{O} \refB Opic, B., Kufner, A.; Hardy-type inequalities; Longman (Harlow); 1990; % has three chapters: % 1. The one-dimensional Hardy inequality % 2. The N-dimensional Hardy inequality % 3. Imbedding theorems for weighted Sobolev spaces %Opitz1964 % carl 16aug02 \rhl{O64} \refJ Opitz, G.; Steigungsmatrizen; \ZAMM; 44; 1964; T52--T54; % divdif table as function in a specific matrix %Oppermann1969 % WhittakerRobinson23:20 08apr04 \rhl{} \refJ Oppermann, ?.; xxx; J. Inst.\ Act.; 15; 1869; 146--xxx; % early mention of the term `divided difference', according to % WhittakerRobinson23:20 %OsbornEyre1979 \rhl{O} \refJ Osborn, T. A., Eyre, D.; Spline function moment methods in three-body scattering; Nuclear Physics, A; 327; 1979; 125--138; %OsipenkoStessin1992 % carl \rhl{O} \refJ Osipenko, K. Yu., Stessin, M. I.; On some problems of optimal recovery of analytic and harmonic functions from inaccurate data; \JAT; 70; 1992; 206--228; %Oskolkov1979 % foucart 03apr06 \rhl{} \refQ Oskolkov, K. I.; The upper bound of the norms of orthogonal projections onto subspaces of polygonals; (Approximations Theory (Warsaw, 1975)), xxx (ed.), Banach Center Publ., (4, PWN, Warsaw); 1979; 177--183; % orthoprojectors onto linear splines %Oskolkov1979a % carl 26oct95 \rhl{O} \refQ Oskolkov, K. I.; The upper bound of the norms of orthogonal projections onto subspaces of polygonals; (Approximation Theory), xxx (ed.), Banach Center Publications, Vol.\ 4, PWN -- Polish Scientific Publishers (Warsaw); 1979; 177--183; % proves that the norm of the orthogonal projector onto linear splines as a % map on continuous functions is at least $3 - 4/(3 2^n)$ if there are $n+1$ % polynomial pieces. Uses facts about the inverse of a tridiagonal matrix. %Oskolkov1979b % carl 26oct95 5dec96 \rhl{O} \refJ Oskolkov, K. I.; Polygonal approximation of functions of two variables; \MUSSRS; 35(6); 1979; 851--861; % With $f$ a (1,1)-periodic bivariate function of H\"older class $H_p^\alpha$ % there exists, for each $n$, some continuous (1,1)-periodic plinear $f_n$ % on some triangulation of the unit square of no more than $n^2$ pieces which % is within $O(n^{-\alpha})$ of $f$ uniformly. %OstapenkoKhazankina1968 % larry \rhl{O} \refJ Ostapenko, V. N., Khazankina, N. P.; A method of signal approximation; Soviet Automat.\ Control; 13; 1968; 59--64; %OstapenkoKhazankina1969 \rhl{O} \refJ Ostapenko, V. N., Khazankina, N. P.; Piecewise polynomial functions and their applications in the algorithmization of electrotechnical calculations; Nekofor.\ Prikl.\ Vopr.\ Mat.\ Kiev; 4; 1969; 268--274; %Ostrowski1972 % carl 23jun03 \rhl{} \refR Ostrowski, A. M.; On Divided Differences; Basel Mathematical Notes 34; 1972; % uses Genocchi (but attributed to Hermite) to derive expressions for divided % differences with partially confluent arguments; also gives the expansion % [y]f = \sum_{\mu