Minimization methods

A.Yu. Afanasèv, V.A. Novikov and I.I. Prosvirnin, Storage and use of information when seeking minimum and root of functions of one argument, U.S.S.R. Comput. Math. and Math. Phys. 19 (6) (1979) 16--25.

H. Bach, On the downhill method, Comm. ACM 12 (1969) 675--677; 684.

F. Bauhuber, Direkte Verfahren zur Berechnung zur Nullstellen von Polynomen, Computing 5 (1970) 97--118.

V.G. Bunkov, A combined method of determining the zeros of a polynomial, U.S.S.R. Comput. Math. and Math. Phys. 15 (2) (1975) 202--206.

G. Caldwell, A note on the downhill method, J. Assoc. Comput. Mach. 6 (1959) 223--225.

B. Carnahan, H.A. Luther and J.O. Wilkes, Applied Numerical Methods (Wiley, New York, 1969) 141--209.

A.F. Cornock and J.M. Hughes, The evaluation of the complex roots of polynomial equations, Philos. Mag. Ser. 7 34 (1943) 314--320.

J.B.S. de Oliveira and D.M. Claudio, A user directed approach to finding roots of polynomials, in: E. Kaucher et al., Eds., Computer Arithmetic, Scientific Computation and Mathematical Modelling (Baltzer, Basel, 1991) 351--366.

A.A. Goldstein, Cauchy's method of minimization, Numer. Math. 4 (1962) 146--150.

J.A. Grant and G.D. Hitchins, Two algorithms for the solution of polynomial equations to limiting machine precision, Comput. J. 18 (1975) 258--263.

J.A. Grant and G.D. Hitchins, An always convergent minimization technique for the solution of polynomial equations, J. Inst. Math. Appl. 8 (1971) 122--129.

J.A. Grant and A.A. Rahman, Determination of the zeros of a linear combination of generalized polynomials, J. Comput. Appl. Math. 42 (1992) 269--278.

P. Henrici, Applied and Computational Complex Analysis, Vol. I (Wiley, New York, 1974) 433--552.

P. Henrici, Methods of descent for polynomial equations, in: H. Werner et al., Eds., Computational Aspects of Complex Analysis (Reidel, Dordrecht, 1983) 133--147.

P. Kokotovic and D.D. Siljak, Automatic analog solution of algebraic equations and plotting of root loci by generalized Mitrovic's method, IEEE Trans. Appl. Indust. 83 (1964) 324--328.

G.N. Lance, Numerical Methods for High Speed Computers (Iliffe, London, 1960) 123--137.

G.N. Lance, Solution of algebraic and transcendental equations on an automatic digital computer, J. Assoc. Comput. Mach. 6 (1959) 97--101.

D.H. Lehmer, Search procedures for polynomial equation solving, in: B. Dejon and P. Henrici, Eds., Constructive Aspects of the Fundamental Theorem of Algebra (Wiley/Interscience, New York, 1969) 193--208.

L. Levine and H.F. Meissinger, An automatic analog computer method for solving polynomials and finding root loci, in: National Convention Record, 4 (Inst. Radio Engrgs., 1957) 164--172.

G.R. Lindfield and J.E.T. Penny, Microcomputers in Numerical Analysis (Wiley, New York, 1989) Chapter 2.

W.C. Lynge, A combined method for polynomial roots using modified Newton-Raphson with minimum searching, J. Comput. Appl. Math. 42 (1992) 339--355.

K. Madsen and J.K. Reid, Fortran subroutines for finding polynomial zeros, Harwell Report AERE-R 7986, H.M. Stationery Office, London, 1975.

K. Madsen, A root-finding algorithm based on Newton's method, BIT 13 (1973) 71--75.

D. Martin, On continuous descent functions for polynomial equations, Z. Angew. Math. Phys. 27 (1976) 863--866.

J.B. Moore and K.T. Clark, A simple convergent algorithm for rapid solution of polynomial equations, IEEE Trans. Computing 19 (1970) 79--80.

J.B. Moore, A convergent algorithm for solving polynomial equations, J. Assoc. Comput. Mach. 14 (1967) 311--315.

J.B. Moore, A consistently rapid algorithm for solving polynomial equations, J. Inst. Math. Appl. 17 (1976) 99--110.

K. Murota, Global convergence of a modified Newton's iteration for algebraic equations, SIAM J. Numer. Anal. 19 (1982) 793--799.

M. Onoe, Triangular walk pattern for the downhill method of solving transcendental equations, Comm. ACM 5 (1962) 399.

A.M. Ostrowski, Solution of Equations and Systems of Equations (Academic Press, New York, 2nd ed., 1966).

A.M. Ostrowski, A method for automatic solution of algebraic equations, in: B. Dejon and P. Henrici, Eds., Constructive Aspects of the Fundamental Equation of Algebra (Wiley/Interscience, New York, 1969) 209--224.

T. Pomentale, A class of iterative methods for holomorphic functions, Numer. Math. 18 (1971) 193--203.

A. Ralston and P. Rabinowitz, A First Course in Numerical Analysis (McGraw-Hill, New York, 2nd ed., 1987) 354.

S. Ruscheweyh, On a global descent method for polynomials, Numer. Math. 45 (1984) 227--240.

C.E. Schmidt and L.R. Rabiner, A study of techniques for finding the zeros of linear phase FIR digital filters, IEEE Trans. Acoust. Speech Signal Process. 25 (1977) 96--98.

J. Soukup, A method for finding the roots of a polynomial, Numer. Math. 13 (1969) 349--353.

B. Svejgaard, Zeros of polynomials, BIT 7 (1967) 240--246.

I. Tang, Simultaneous determination of quadratic factors by optimization methods, Math. Comput. Simulation 19 (1) (1977) 57--59.

I. Tang, Finding quadratic factors by analog minimisation process, Simulation 26 (1976) 128--129.

K. Viswanathan, Solution of polynomial equations by method of steepest descent, Internat. J. Comput. Math. 2 (1970) 193--200.

V.V. Voevodin, Application of the method of descent for determining all the roots of an algebraic polynomial, U.S.S.R. Comput. Math. and Math. Phys. 1 (2) (1961) 203--213.

J.A. Ward, The downhill method of solving f(z)=0, J. Assoc. Comput. Mach. 4 (1957) 148--149.