Computational Complexity of Iterative Processes

The theory of optimal algorithmic processes is part of computational complexity. This paper deals with analytic computational complexity. The relation between the goodness of an iteration algorithm and its new function evaluation and memory requirements are analyzed. A new conjecture is stated.

[1]  J. Rissanen,et al.  On optimum root-finding algorithms , 1971 .

[2]  Joseph F. Traub Invited papers: The theory of multipoint iteration functions , 1962, ACM '62.

[3]  L. R. Kerr,et al.  On Minimizing the Number of Multiplications Necessary for Matrix Multiplication , 1969 .

[4]  Shmuel Winograd The number of multiplications involved in computing certain functions , 1968, IFIP Congress.

[5]  L. Collatz Functional analysis and numerical mathematics , 1968 .

[6]  P. Jarratt Some efficient fourth order multipoint methods for solving equations , 1969 .

[7]  Richard Edwin Stearns,et al.  Computational complexity of recursive sequences , 1964, SWCT.

[8]  A Feldstein Bounds on order and Ostrowski efficiency for interpolatory iteration algorithms , 1969 .

[9]  J. F. Traub,et al.  On functional iteration and the calculation of roots , 1961, ACM National Meeting.

[10]  Alan Feldstein,et al.  A study of Ostrowski efficiency for composite iteration algorithms , 1969, ACM '69.

[11]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[12]  Webb Miller Toward Abstract Numerical Analysis , 1973, JACM.

[13]  V. Strassen Gaussian elimination is not optimal , 1969 .

[14]  H. T. Kung A bound on the multiplication efficiency of iteration , 1972, STOC '72.

[15]  Joseph F. Traub,et al.  Optimal Iterative Processes: Theorems and Conjectures , 1971, IFIP Congress.

[16]  Robert E. Tarjan,et al.  Planarity Testing in V log V Steps: Extended Abstract , 1971, IFIP Congress.

[17]  E. T. Goodwin SOLUTION OF EQUATIONS AND SYSTEMS OF EQUATIONS (SECOND EDITION) , 1969 .

[18]  R. F. King A Family of Fourth Order Methods for Nonlinear Equations , 1973 .

[19]  Donald E. Knuth,et al.  Mathematical Analysis of Algorithms , 1971, IFIP Congress.

[20]  A. Ostrowski Solution of equations and systems of equations , 1967 .

[21]  M. Rabin Degree of difficulty of computing a function and a partial ordering of recursive sets , 1960 .

[22]  N. S. Barnett,et al.  Private communication , 1969 .

[23]  A. C. Hindmarsh,et al.  Optimality in a Class of Rootfinding Algorithms , 1972 .

[24]  Marvin Minsky,et al.  Form and Content in Computer Science (1970 ACM turing lecture) , 1970, JACM.