The files are now also available in

If you have trouble because of file contamination, specify

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;

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;

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;

The B-spline recurrence relations of Chakalov and of Popoviciu

Carl de Boor and Allan Pinkus

mar 2003

\JAT; 124(1); 2003; 115--123;

Spline Basics

Carl de Boor

dec 2000

Chapter 6 in \Cagdhand; see (cagd.snu.ac.kr/main.html)

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)

On mixed interpolating-smoothing splines and the $\nu$-spline

Scott Kersey

jun 1999

Best near-interpolation by curves: existence and convergence

Scott Kersey

apr 1999

Best near-interpolation by curves: optimality conditions

Scott Kersey

apr 1999

Calculation of the smoothing spline with weighted roughness measure

Carl de Boor

sep 1998

Math.\ Models Methods Appl.\ Sci.; 11(1); 2001; 33--41;

On the Meir/Sharma/Hall/Meyer analysis of the spline interpolation error

Carl de Boor

December 1996

Appeared in:

\Powellfest; 47--58;

The multiplicity of a spline zero

Carl de Boor

December 1995

January 96 (reflect referee's comments)

appeared in

\AoNM; 4; 1997; 229--238;

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;

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).

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

$B$--form basics;

Carl de Boor

1986

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.

Convergence of cubic spline interpolation with the not-a-knot condition

Carl de Boor

1985

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;

On a max-norm bound for the least-squares spline approximant

Carl de Boor

1980

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;

How does Agee's smoothing method work?

Carl de Boor

1978

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;

299--302;

Stability of interpolating elastica;

Michael Golomb

may 1978

has appeared as: MRC TSR #1852;

Splines as linear combinations of B-splines. A Survey

Carl de Boor

1976

has appeared in \TexasII; 1--47;

% corrected version (with updated references) 19sep97

% left off an extraneous label (6.1) 01aug03

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

1975

has appeared:

\MC; 30(136); 1976; 765--771;

http://www.ams.org/journals/mcom/1976-30-136/S0025-5718-1976-0425432-1/S0025-5718-1976-0425432-1.pdf

On calculating with B-splines II. Integration;

C. de Boor, T. Lyche, L. L. Schumaker;

1975

(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;

On local linear functionals which vanish at all $B$-splines but one;

Carl de Boor

1975

has appeared in (Theory of Approximation with Applications),

A. G. Law and N. B. Sahney (eds.),

Academic Press (New York); 1976; 120--145;

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

A smooth and local interpolant with ``small'' $k$-th derivative;

Carl de Boor

1975

has appeared in

(Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations),

A. Aziz (ed.), Academic Press (New York); 1975;

177--197;

How small can one make the derivatives of an interpolating function?;

Carl de Boor

1973

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

1973

\AiM, 20(1), 1976, 1--17;

A remark concerning perfect splines;

Carl de Boor;

1973

has appeared as \BAMS; 80(4); 1974; 724--727;

http://www.ams.org/journals/bull/1974-80-04/S0002-9904-1974-13572-X/S0002-9904-1974-13572-X.pdf

Total positivity of the spline collocation matrix;

Carl de Boor;

1974

\JMM, 25(6), 1976, 724--727;

On bounding spline interpolation;

Carl de Boor

1973

\JAT; 14(3); 1975; 191--203;

% added a footnote pointing out that Jia disproved the conjecture, in %Jia88d

The quasi-interpolant as a tool in elementary polynomial spline theory;

Carl de Boor

1973

has appeared in \TexasI; 269--276;

Good approximation by splines with variable knots;

Carl de Boor

1973

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;

On the approximation by $\gamma$-polynomials;

Carl de Boor

1969

has appeared in \MadisonII; 157--183;

On uniform approximation by splines

Carl de Boor

1967

has appeared as \JAT; 1; 1968; 219--235;

4oct08 various misprints have been corrected

Least Squares Cubic Spline Approximation I -- Fixed Knots

Carl de Boor, John R. Rice

CSD TR 20 April 1968

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;

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

On splines and their minimum properties;

Carl de Boor and Robert E. Lynch

1965

has appeared in

\JMM; 15; 1966; 953--969;

Nonlinear inrterpolation by splines, pseudosplines and elastica;

Garrett Birkhoff, Hermann Burchard, Donald Thomas;

february 1965

VERY LONG FILE, 4.8Mb

GMR 468, General Motors Research Laboratories (Warren MI); 1965;1

Error bounds for spline interpolation;

Garrett Birkhoff & Carl de Boor;

1964

\JMM, 13(5), 1964, 827--835;

Piecewise polynomial interpolation and approximation;

Garrett Birkhoff and Carl R. de Boor;

1965

VERY LONG FILE, 8.1Mb

has appeared in

\Generalmotors; 164--190;

Best approximation properties of spline functions of odd degree;

Carl de Boor;

1963

\JMM, 12(5), 1963, 747--750;

List of publications of I. J. Schoenberg

(Carl de Boor)

1987

updated 10mar09