By George Biddell Airy
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Extra info for A treatise on trigonometry
1 3 ) . Yj). REFERENCES 1. N. I. Akhiezer and I. M. Glazman (1963), Theory of linear operators in Hilbert Space, vol. II, Fredrick Ungar Publ. , New York. 2. N. Aronszajn and W. F. Donoghue, Jr. (1957), On exponential repre sentations of analytic functions in the upper half-plane with positive imaginary part, Journal d Analyse Mathematique, vol. 5 321-388. v S. Barnett and D. D. Siljak (1977)> Routh algorithm: a centennial survey, SIAM Rev. 1 9 , 472-489. 1 3. 4. V. Belevitch (1968), Classical network theory, Holden-Day, San Francisco.
10, 191-236. 7. C. W. Cryer (1973), A new class of highly-stable methods5 A -stable methods, BIT 13, 153-159. 8. G. G. Dahlquist (1956), Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand 4, 33-53. 9. 10. (1963), A special stability problem for linear multistep methods, BIT 3, 27-43. (1975), Error analysis for a class of methods for stiff non linear initial value problems, Numerical Analysis Dundee, Springer Lecture Notes in Mathematics no.
N. 5) holds with computation, _ . u - 1,2 ,. . ,n. n. ) goes Its condition number grows exponentially, max cond E l£|Kn , n -> . 6) y The best conditioned root is ^ = 1, with a condition number that grows very slowly, 2 cond £^ ^ n , n . 7) It is instructive to observe what happens if one of the coefficients u. in 1 n (x-v) = x + u x + ... + u, , v=l say the coefficient u, , k = [(n+3)/2], is continuously per0 turbed, n n n u, (t) = 0 K (l+t)u, 0 1 , 0 < t < e , ~ ~ K all other coefficients being held constant.
A treatise on trigonometry by George Biddell Airy