Quadratic Spline.
Show how to obtain the constants below (a1,b1,c1 etc...) from the
equations above through algebra particularly substitution or
elimination. Please show complete solution and and also neat
handwriting.
Quadratic Spline Show How To Obtain The Constants Below A1 B1 C1 Etc From The Equations Above Through Algebra Part 1 (62.59 KiB) Viewed 18 times
eqn 1 Condition #1: From the Interior knots: Q, R at point Q: (4)2 + b(4) + C1 = 2 az(4)2 + b (4) + C2 = 2 at point R: az(7)2 + b2(7) + C2 = 8 egn 3 az(7)2 + b3(7) + C3 = 8 egn 2 ------- eqn 4 eqn 5 Condition #2: From the exterior knots: P, S At point P: a(3)+ b (3) + C1 = 5 At point S: a3(92 + b3(9) + c3 = 6 Condition #3: First derivatives of the interior knots are equal 2a,x + b = 2a2x + b2 ----- eqn 7 2a2x + b2 = 2a3x + bg eqn 8 egn 6 Condition #4: a, = 0 eqn 9 From the 9 equations, by solving for the unknowns algebraically, we will get the following: a1 = 0 a2 = 15/9 a3 = -4 b1 = -3 b2 = -49/3 b3 = 63 c1 = 14 c2 = 122/3 c3 = -237
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