#### VARIATIONAL THEORY OF SPLINES

that we've found may be relevant to this textbook.
Author: Anatoly Yu Bezhaev, Vladimir A. Vasilenko
ISBN: 9780306466427

• Notes on Least Squares Cubic Splines The documentation of the Spline Toolbox provides a one-line command for computing the cubic spline that best ts data in a least squares sense. Specically, sp = spline(b,y(:)/spline(b,eye(length(b),x(:); returns th

• COMPUTER SCIENCE 340 ASSIGNMENT #10 DUE MONDAY JULY 30, 2007 (in class) 1. Determine values of a, b, c and d so that x 2 + x + 1 , Q( x) = ax 2 + bx + c , dx 2 - 1 , 0.5 x 1 1 x 2 2 x3 is a quadratic spline function on [0.5, 3]. (Note: Q(x)

• Stanford Exploration Project, Report 105, September 5, 2000, pages 2383 22 Stanford Exploration Project, Report 105, September 5, 2000, pages 2383 Inverse B-spline interpolation Sergey Fomel1 ABSTRACT B-splines provide an accurate and efficient m

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• CS 465 Program 3: Model out: Friday 21 September 2007 due: Monday 15 October 2007 Wednesday 17 October 2007 1 Introduction In this assignment you will work on a 3D modeling system that uses simple primitives and curved surfaces organized in a tran

• CS 465 Program 4: Modeler out: 28 October 2005 due: 15 November 2005 1 Introduction In this assignment you will work on a 3D modeling system that uses simple primitives and curved surfaces organized in a transformation hierarchy. The framework pro

• NAME: Login name: Computer Science 426 Midterm 2 4/29/04, 1:30PM-2:50PM This test is 5 questions of equal weight. Do all of your work on these pages (use the back for scratch space), giving the answer in the space provided. This is a closed-book ex

• COMPUTER SCIENCE 349A Handout Number 24 CUBIC SPLINE INTERPOLANTS The following definition is the same as given in points 1-5 on pages 501-502 of the textbook, but is more precise. Definition x0 , x1 , K , x n with xi < xi +1 , and f ( x0 ), f ( x

• Announcements BSplines Lecture #26 Monday, November 3rd, 2008 Programming Assignment #3 is due Wednesday Higher-order Curves de Casteljaus algorithm works for any number of initial points. 4 points lead to a 3rd-order curve, 5 points lead to a 4th

• CS 465 Program 4: Modeller out: 30 October 2004 due: 16 November 2004 1 Introduction In this assignment you will work on a simple 3D modelling system that uses simple primitives and curved surfaces organized in a transformation hierarchy and provi

• ACM 106a, Problem Set 3: Solutions Ari Stern, TA November 30, 2007 Theory 1. (a) Between two knots x i , x i +1 , the energy functional is given by the single term x i +1 E [y] = xi y (x) + 2 y (x) i 2 2 d x. Now take a variation y of y; to s

• L. Vandenberghe EE236B Winter 2009 Additional problems for homework assignment #2 1. The geometric mean f (x) = ( k xk )1/n with dom f = Rn is concave, as shown on + page 74 of the textbook. Extend the proof to show that the function n f (x) = k=