## 2021: Third EditionTea Time Numerical Analysis Experiences in Mathematics

#### Errata, Last updated 16 January 2021

• PP. 3-4,6,9: the roles of tilde p and tilde p ^ ** should be made clear. tilde p represents any approximation (generally calculated using floating-point arithmetic). tilde p ^ ** exclusively represents an approximation calculated using exact arithmetic.
• P. 9 exercise 24 part b: (1) the sum should be from 1 to 9; and (2) 0.2071647018159241499410798569 should be 0.3550449718187918680449850763.
• P. 18 exercise 27 part g: T_2(x) should be T_3(x).
• P. 24 end of Crumpet 8: In the last line, "not" should be "no".
• P. 38 exercise 20: A better demonstration of the instability of calculating << c_n >> would be to calculate c_50.
• Section 2.1: Reference to maximum number of iterations should be deleted. It has been removed from the pseudo-code.
• P. 47 exercise 20b: f should be g.
• P. 48 exercise 29: Step 4 should return i, not N_0.
• P. 48 exercise 30a: The equation should be x-2^x+.95=0.
• P. 58 exercise 3b: Should read f(x)=ln(2e^x)/2.
• P. 58 exercise 17: The roles of f and g should be swapped.
• P. 59 exercise 20: "any fixed point" should read "any nonzero fixed point".
• P. 59 exercise 22: The assumption g'(hat x) ne 0 should be added.
• P. 67 exercise 3: The Octave logo should be added.
• P. 75 exercise 14: One of the "the"s should be stricken.
• P. 249 solution 26 part f: The inequality 64/625 le 64/1125 le 64/6561 should be 64/6561 le 64/1125 le 64/625.
• P. 250 solution 30b: The derivative of g is missing the exponential factor, e^(-xi^2), in two separate places.
• P. 334 sec 2.2 answer 4c: root(5)((4-3x^2)/2) should be replaced by root(5)((4-6x^2)/3).
• P. 334 sec 2.2 answer 4f: Each instance of (x^2-5x+1) should be replaced by -(x^2-5x+1).
• P. 335 sec 2.3 answer 18: Should read, "Yes. Aitken's delta-squared method is designed to speed up linearly convergent sequences and << a_n >> is linearly convergent."
• P. 336 sec 2.4 answer 20: Is wrong. Needs to be corrected.