papers on univariate splines at

These files can be obtained by anonymous from The files are postscript, and are also available as compress(ed) files, as indicated by the subscript .Z, to be uncompress(ed) before using, as well as as (shorter) gzip(ed) files, as indicated by the subscript .gz, to be extracted by gzip -d .
The files are now also available in pdf. For those from before '98, these pdf files might not look very good in an acrobat reader, but will print just fine.
If you have trouble because of file contamination, specify binary as your first command in ftp.
The files are in order of increasing age.

Elastic Splines III: Existence of stable nonlinear splines;
Albert Borb\'ely & Michael J. Johnson
december 2018;

Elastic Splines II: Unicity of optimal s-curves and curvature continuity;
Albert Borb\'ely & Michael J. Johnson
august 2017

A constructive framework for minimal energy planar curves;
Michael J. Johnson & Hakim S. Johnson;
december 2016
\AMC (Applied Mathematics and Computation); 276; 2016; 172--181;

A comment on Ewald Quak's "About B-splines";
Carl de Boor
october 2016
\JNAAT;45(1); 2016; 84--86;

Elastic splines I: Existence;
Albert Borb\'ely & Michael J. Johnson;
january 2014
has appeared:
\CA; 40; 2914; 189--218;

Minimal degree univariate piecewise polynomials with prescribed Sobolev regularity;
Amal Al-Rashdan, Michael J. Johnson
october 2011
\JAT; 164(1); 2012; 1--5;

re_shadrin: ps ps.Z ps.gz pdf
On the (bi)infinite case of Shadrin's theorem concerning the $L_\infty$-boundedness of the $L_2$-spline projector;
Carl de Boor
july 2011
has appeared in the Subbotin 75th anniversary volume
Trudy Instituta Matematiki i Mekhaniki UrO RAN; 17(3); 2011, 25--29;

asympterr: ps ps.Z ps.gz pdf
An asymptotic expansion for the error in a linear map that reproduces polynomials of a certain order
Carl de Boor
apr 2003
\JAT; 134; 2005; 171--174;

chakpop: ps ps.Z ps.gz pdf
The B-spline recurrence relations of Chakalov and of Popoviciu
Carl de Boor and Allan Pinkus
mar 2003
\JAT; 124(1); 2003; 115--123;

cagdhand: ps ps.Z ps.gz pdf
Spline Basics
Carl de Boor
dec 2000
Chapter 6 in \Cagdhand; see (

inverse_basis: ps ps.Z ps.gz pdf
What is the inverse of a basis?
Carl de Boor
sep 2000
BIT; 41(5); 2001; 880--890;
(the printed version contains a random 7 right in the middle of (4.2), the most
important formula of the paper, and an extra p in the first display on page 889)

mixed: ps ps.Z ps.gz pdf
On mixed interpolating-smoothing splines and the $\nu$-spline
Scott Kersey
jun 1999

exists: ps ps.Z ps.gz pdf
Best near-interpolation by curves: existence and convergence
Scott Kersey
apr 1999

optimality: ps ps.Z ps.gz pdf
Best near-interpolation by curves: optimality conditions
Scott Kersey
apr 1999

smooth: ps ps.Z ps.gz pdf
Calculation of the smoothing spline with weighted roughness measure
Carl de Boor
sep 1998
Math.\ Models Methods Appl.\ Sci.; 11(1); 2001; 33--41;

splerr: ps ps.Z ps.gz pdf
On the Meir/Sharma/Hall/Meyer analysis of the spline interpolation error
Carl de Boor
December 1996
Appeared in:
\Powellfest; 47--58;

zerocount: ps ps.Z ps.gz pdf
The multiplicity of a spline zero
Carl de Boor
December 1995
January 96 (reflect referee's comments)
appeared in
\AoNM; 4; 1997; 229--238;

chebspline: ps ps.Z ps.gz pdf
The exact condition of the B-spline basis may be hard to determine
Carl de Boor
July 1988
has appeared in \JAT; 60; 1990; 344--359;

bsplloccond: ps ps.Z ps.gz pdf
The condition of the B-spline basis for polynomials
Carl de Boor
April 1987
has appeared as
\SJNA; 25(1); 1988; 148--152;
but the journal's final computer-aided processing messed up the paper through
the omission of various words (that happened to lie beyond column 80 on a
line in the TeX file).

bsplbasic: ps ps.Z ps.gz pdf
B-spline basics
Carl de Boor
MRC 2952, 1986
in (Fundamental Developments of Computer-Aided Geometric Modeling),
Les Piegl (ed.), Academic Press (London) 1993; 27--49;
% Corrected (in Section 12) on 04 mar 96.
% Scaling of figures adjusted and misprints corrected on 03 jun 96
% A misprint corrected (and adjusted to current tex-macros) on 06 jun 96
% A misprint corrected on 12feb98
% A reference updated 27apr09 but the change to (2.4b) made then rescinded on 30mar10

BBform: ps ps.Z ps.gz pdf
$B$--form basics;
Carl de Boor
in (Geometric Modeling: Algorithms and New Trends),
G. E. Farin (ed.),
SIAM Publications (Philadelphia); 1987; 131--148;
% 30nov09 supplied the missing Figure 3, and corrected a typo in (3.3) and in
% last display before Section 6.

notaknot: ps ps.Z ps.gz pdf
Convergence of cubic spline interpolation with the not-a-knot condition
Carl de Boor
MRC TSR 2876, October 1985

A geometric proof of total positivity for spline interpolation
Carl de Boor and Ron DeVore
March 1984
has appeared in \MC; 45(172); 1985; 497--504;

Local piecewise polynomial projection methods for an O.D.E.\ which give high-order convergence at knots
Carl de Boor and Blair Swartz
summer 1980
has appeared in \MC; 36; 1981; 21--33;

maxnormbound: ps ps.Z ps.gz pdf
On a max-norm bound for the least-squares spline approximant
Carl de Boor
has appeared in
(Approximation and Function Spaces),
C. Ciesielski (ed.),
North Holland (Amsterdam); 1981; 163--175;

Collocation approximation to eigenvalues of an ordinary differential equation: Numerical illustrations;
Carl de Boor and Blair Swartz
March 1980
has appeared in \MC; 36(153); 1981; 1--19;

Collocation approximation to eigenvalues of an ordinary differential equation: The principle of the thing;
Carl de Boor and Blair Swartz
March 1979
has appeared in \MC; 35(151); 1980; 679--694;

agee: ps ps.Z ps.gz pdf
How does Agee's smoothing method work?
Carl de Boor
has appeared in
(Proceedings of the 1979 Army Numerical Analysis and Computers Conference),
xxx (ed.), ARO Rept.\ 79-3, Army Research Office (Triangle Park NC); 1979;

Stability of interpolating elastica;
Michael Golomb
may 1978
has appeared as: MRC TSR #1852;

survey76: ps ps.Z ps.gz pdf
Splines as linear combinations of B-splines. A Survey
Carl de Boor
has appeared in \TexasII; 1--47;
% corrected version (with updated references) 19sep97
% left off an extraneous label (6.1) 01aug03

oddbiinf: ps ps.Z ps.gz pdf
Odd-degree spline interpolation at a biinfinite knot sequence
Carl de Boor
\Tex-version of MRC TSR #1666, August 1976
has appeared in \BonnI; 30--53;

A bound on the $L_\infty$-norm of $L_2$-approximation by splines in terms of a global mesh ratio;
Carl de Boor
has appeared:
\MC; 30(136); 1976; 765--771;

On calculating with B-splines II. Integration;
C. de Boor, T. Lyche, L. L. Schumaker;
(warning: it's a 10Mb file)
in: Numerische Methoden der Approximationstheorie Vol.\ 3, ISNM 30),
L. Collatz, G. Meinardus, and H. Werner (eds.),
Birk\-h\"auser Verlag (Basel); 1976; 123--146;

loclinfl: ps ps.Z ps.gz pdf
On local linear functionals which vanish at all $B$-splines but one;
Carl de Boor
has appeared in (Theory of Approximation with Applications),
A. G. Law and N. B. Sahney (eds.),
Academic Press (New York); 1976; 120--145;

budanfourier: ps ps.Z ps.gz pdf
Cardinal interpolation and spline functions VIII: The Budan Fourier theorem for splines and applications;
Carl de Boor and I. J. Schoenberg
feb 1975
has appeared in (Lecture Notes in Mathematics 501), K. B\"ohmer (ed),
Springer-Verlag (Berlin); 1976; 1--77;
% corrected jul2000 a la KohlerNikolov95a

smallderiv: ps ps.Z ps.gz pdf
A smooth and local interpolant with ``small'' $k$-th derivative;
Carl de Boor
has appeared in
(Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations),
A. Aziz (ed.), Academic Press (New York); 1975;

howsmall: ps ps.Z ps.gz pdf
How small can one make the derivatives of an interpolating function?;
Carl de Boor
has appeared as \JAT; 13; 1975; 105--116;
% corrected version (with updated references) 22oct99

On cubic spline functions that vanish at all knots;
Carl de Boor
\AiM, 20(1), 1976, 1--17;

A remark concerning perfect splines;
Carl de Boor;
has appeared as \BAMS; 80(4); 1974; 724--727;

Total positivity of the spline collocation matrix;
Carl de Boor;
\JMM, 25(6), 1976, 724--727;

splbound: ps ps.Z ps.gz pdf
On bounding spline interpolation;
Carl de Boor
\JAT; 14(3); 1975; 191--203;
% added a footnote pointing out that Jia disproved the conjecture, in %Jia88d

quasiint: ps ps.Z ps.gz pdf
The quasi-interpolant as a tool in elementary polynomial spline theory;
Carl de Boor
has appeared in \TexasI; 269--276;

goodappr: ps ps.Z ps.gz pdf
Good approximation by splines with variable knots;
Carl de Boor
has appeared in \EdmontonI; 57--72;

Carl de Boor and James W. Daniel
Splines with nonnegative $B$-spline coefficients
april 1973
has appeared: \MC; 28(126); 1974; 565--568;

Subroutine Package for Calculating with B-splines;
Carl de Boor
August 1971
report LA-4728-MS Los Alamos scientific laboratory,
An extended version has appeared as
``Package for calculating with B-splines'', \SJNA, 14, 1977, 441--472.

On calculating with $B$-splines;
Carl de Boor
september 1970
\JAT; 6; 1972; 50--62;

gamma: ps ps.Z ps.gz pdf
On the approximation by $\gamma$-polynomials;
Carl de Boor
has appeared in \MadisonII; 157--183;

unifappr: ps ps.Z ps.gz pdf
On uniform approximation by splines
Carl de Boor
has appeared as \JAT; 1; 1968; 219--235;
4oct08 various misprints have been corrected

tr20: ps ps.Z ps.gz pdf
Least Squares Cubic Spline Approximation I -- Fixed Knots
Carl de Boor, John R. Rice
CSD TR 20 April 1968

tr21: ps ps.Z ps.gz pdf
Least Squares Cubic Spline Approximation II -- Variable Knots
Carl de Boor, John R. Rice
CSD TR 21 April 1968
% error in NUBAS corrected 3oct01

On local spline approximation by moments;
Carl de Boor
Sep 1966
has appeared in
\JMM; 17; 1968; 729--735;

deboorphd: ps ps.Z ps.gz pdf
The method of projections as applied to the numerical solution of two point boundary value problems using cubic splines
Carl de Boor Ph.D. thesis, Univ.\ Michigan
August 1966
% corrected version (with updated references) 4apr96

lynch: ps ps.Z ps.gz pdf
On splines and their minimum properties;
Carl de Boor and Robert E. Lynch
has appeared in
\JMM; 15; 1966; 953--969;

Nonlinear inrterpolation by splines, pseudosplines and elastica;
Garrett Birkhoff, Hermann Burchard, Donald Thomas;
february 1965
GMR 468, General Motors Research Laboratories (Warren MI); 1965;1

Error bounds for spline interpolation;
Garrett Birkhoff & Carl de Boor;
\JMM, 13(5), 1964, 827--835;

Piecewise polynomial interpolation and approximation;
Garrett Birkhoff and Carl R. de Boor;
has appeared in
\Generalmotors; 164--190;

Best approximation properties of spline functions of odd degree;
Carl de Boor;
\JMM, 12(5), 1963, 747--750;

isobib: ps ps.Z ps.gz pdf
List of publications of I. J. Schoenberg
(Carl de Boor)
updated 10mar09