2440 



Numerical solution of equations 



2440 



Approximate determination of roots, continued. 

 A. Q. G. C. Mess. Mth. 4 (1868) 132-. 



D g. Ts. Mt. Fys. 4 (1871) 201-. 



Laguerre, . N. A. Mth. 3 (1884) 113-. 

 Bugaev, N. V. [1894] Eec. Mth. (Moscou) 18 



(1896) 289- ; Fschr. Mth. (1896) 70-. 

 Laisant, C. A. As. Fr. C. B. (1895) (Ft. 2) 



220- . 

 Bugaev, N. V. [1896] Eec. Mth. (Moscou) 19 



(1897) 421 (bis)- ; Fschr. Mth. (1897) 96. 

 Lemeray, E. M. N. A. Mth. 17 (1898) 534-. 

 of cubic equations by continued fractions. 



Sang, E. Edinb. E. S. P. 32 (1887) 311-. 



(1 + p) n 1 



equation A = v 2 . Ryley, E. Assur. 



Mg. [1 (* 1851)] 332-. 

 with real roots only. Laguerre, E. C. 



E. 79 (1874) 522-; N. A. Mth. 19 (1880) 

 161-, 193-. 



(Laguerre). Hermite, C. 



Em. N. Line. Mm. 3 (1888) 155-. 

 ( ). Borel, E. fill. Sc. 



Mth. 22 (1898) 11-. 

 imaginary roots. Bonnet, 0. N. A. Mth. 4 



(1845) 164-, 388-; 12 (1853) 243-. 



, Lagrange's method. Cavalieri San- 

 Bertolo, N. Em. At. 4 (1850-51) 1-. 



incommensurable roots. Fauche-Prunelle, A, 



Grenoble Ac. Delph. Bll. 1 (1846) 563-. 

 irrational roots. Voll, W. Oken Isis (1826) 



490-. 

 real roots. Piobert, . N. A. Mth. 10 (1851) 



174-. 



. Buchwaldt, F. Mth. Ts. 2 (1860) 73-. 



. Janni, G. G. Mt. 8 (1870) 157-. 



of equation x n +px + q = 0. Kjeldgaard, 



A. {xn) Ts. Mth. 4 (1880) 135-. 

 , methods of Cauchy and Newton. Moigno, 



F. N. A. Mth. 10 (1851) 14-. 



in series of aliquot parts. Homer, J. QJ. 



Mth. 3 (1860) 251-. 

 Simpson's method. Pessuti, G. [1806] Mod. 



S. It. Mm. 13 (1807) 193-. 

 singular case. Gergonne, J. D. Gergonne A. 



Mth. 10 (1819-20) 122-. 



Budan's method. Gergonne, J. D. Gergonne 



A. Mth. 4 (1813-14) 115-. 

 . Ferroni, P. [1823] Mod. S. It. Mm. 20 



(1828) 17-. 

 Cauchy 's modification of Newton's method. 



Housel, . N. A. Mth. 15 (1856) 244-. 

 Continued fractions applied to determining 



two roots simultaneously. Matthiessen, L. 



Schlomilch Z. 6 (1861) 51-. 

 , solution by. Homer, W. G. QJ. Sc. 



21 (1826) 72-, 282-; 22 (1827) 67-, 285-. 

 , . Grebe, E. W. Grunert Arch. 10 



(1847) 345-; 16 (1851) 261-. 

 , . Gomes Teixeira, F. (x) Lisb. J. 



Sc. Mth. 4 (1873) 89-. 

 , . Giinther, S. [1873] (vn) Mth. 



A. 7 (1874) 262-. 

 Convergence of certain series in numerical 



solution of equations. Graeffe, C. H. Crelle 



J. 10 (1833) 288-. 



Convergence of series of approximations to 

 roots of equations. Lemeray, E. M. As. 

 Fr. C. E. (1894) (Pt. 2) 252-. 



for root by Lagrange's theorem. 

 Cauchy, A. L. C. E. 23 (1846) 493-. 



Definite integrals, expression of roots of tri- 

 nomial equations by. Lachtin, L. [1889] 

 Eec. Mth. (Moscou) 15 (1891) 61-. 



, solution by. Jacobi, C. G. J. Crelle 



J. 2 (1827) 1-. 



, . Hoppe, E. Schlomilch Z. 3 



(1858) 173-. 



, . Kretkowski, W. [1881] (xn) Krk. 



Ak. (Mt.-Prz.) Pam. 7 (1882) 158-. 



Derived functions and numerical solution of 

 equations. Mlasojedov, A. N. Eec. Mth. 

 (Moscou) 12 (1885) 757- ; Fschr. Mth. (1886) 



Differential equations, solution by. Heymann, 

 W. Z. Mth. Ps. 31 (1886) 102-, 129-. 



Eisenstein's theorem on series for root of 

 algebraic equation. Hermite, C. L. Mth. 

 S. P. 7 (1875-76) 173-. 



. Gomes Teixeira, F. 



Arch. Mth. Ps. 3 (1886) 315-. 



Equation A = (l + x) m (l + bx), numerical solu- 

 tion, x being a small fraction. Badell, . 

 Grunert Arch. 2 (1842) 122-. 



= (-)(-). . Lind- 



man, C. F. Grunert Arch. 23 (1854) 445-. 



Equations a 2 + fee = 16, 6 2 + ac=17, c 2 + o6=18, 

 approximate solution. Bute, . Thomson 

 A. Ph. 5 (1815) 53-. 



in Bangma's "Algebra voor de Scholen." 

 Schmidt, J. B. Amst. Mengelwerk 2 (1816) 

 153-. 



, continued fractions for whose roots terminate 



in same quotients. Serret, J. A. Liouv. J. 



Mth. 15 (1850) 152-. 

 , order of which is power of prime number. 



Betti, E. Tortolini A. 6 (1855) 260- ; C. E. 



48 (1859) 182-. 

 , . Mathieu, E. 



Tortolini A. 4 (1861) 113-. 



with secondary (imaginary) roots. Zielinski, 

 A. Des Moines Anal. 3 (1876) 52-. 



, 2nd order, exhibition of both roots in one 



series of converging fractions. Sang, E. 



Edinb. E. S. P. 4 (1862) 70-. 

 , , solution by continued fractions. 



Lebesgue, V. A. Liouv. J. Mth. 5 (1840) 



281-. 

 , , successive approximation, cases. 



St Germain, A. de. N. A. Mth. 13 (1874) 



401-. 

 , , where coefficient of x 2 is small. 



Gerono, G. C. N. A. Mth. 16 (1857) 436-. 

 , 3rd order, development of roots in continued 



fractions. Sarrus, F. Gergonne A. Mth. 10 



(1819-20) 189-. 

 , , irreducible case, development of 



roots in continued fraction. Clausen, T. 



As. Nr. 19 (1842) 241- ; Grunert Arch. 2 



(1842) 446- (with additions by Grunert). 

 , , numerical solution. Maulbon 



d'Arbaumont, . Epinal (Vosg.) A. 2 (1834) 



637-. 



175 



