A variable dimension fixed point algorithm and the orientation of simplices
- Yoshitsugu Yamamoto
- … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
A variable dimension algorithm with integer labelling is proposed for solving systems ofn equations inn variables. The algorithm is an integer labelling version of the 2-ray algorithm proposed by the author. The orientation of lower dimensional simplices is studied and is shown to be preserved along a sequence of adjacent simplices.
- E. Allgower and K. Georg, “Simplicial and continuation methods for approximating fixed points and solutions to systems of equations”,SIAM Review 22 (1980) 28–85. CrossRef
- B.C. Eaves, “A short course in solving equations with PL homotopies”,SIAM-AMS Proceedings 9 (1976) 73–143.
- B.C. Eaves and H. Scarf, “The solution of systems of piecewise linear equations”,Mathematics of Operations Research 1 (1976) 1–27.
- M. Kojima and Y. Yamamoto, “A unified approach to the implementation of several restart fixed point algorithms and a new variable dimension algorithm”,Mathematical Programming 28 (1984) 288–328.
- G. van der Laan, “Simplicial fixed point algorithms”, Ph.D. Dissertation, Free University (Amsterdam, 1980).
- G. van der Laan, “On the existence and approximation of zeroes”,Mathematical Programing 28 (1984) 1–24.
- G. van der Laan and A.J.J. Talman, “A restart algorithm for computing fixed point without extra dimension”,Mathematical Programming 17 (1979) 74–84. CrossRef
- G. van der Laan and A.J.J. Talman, “A restart algorithm without an artificial level for computing fixed points on unbounded regions”, in: H.-O. Peitgen and H.-O. Walther, eds.,Functional Differential Equations and Approximation of Fixed Points, Lecture Notes in Mathematics 730 (Springer Berlin, 1979) pp. 247–256. CrossRef
- G. van der Laan and A.J.J. Talman, “Convergence and properties of recent variable dimension algorithms”, in: W. Forster, ed.,Numerical Solution of Highly Nonlinear Problems, Fixed Point Algoroithms and Complementarity Problems (North-Holland, New York, 1980) pp. 3–36.
- G. van der Laan and A.J.J. Talman, “A class of simplicial restart fixed point algorithms without an extra dimension”,Mathematical Programming 20 (1981) 33–48. CrossRef
- R. Saigal, “A homotopy for solving large, sparse and structured fixed point problems”,Mathematics of Operations Research 8 (1983) 557–578.
- M.J. Todd, “Orientation in complementary pivoting”Mathematics of Operations Research 1 (1976) 54–66. CrossRef
- A.H. Wright, “The octahedral algorithm, a new simplicial fixed point algorithm”,Mathematical Programming 21 (1981) 47–69. CrossRef
- Y. Yamamoto, “A new variable dimension algorithm for the fixed point problem”,Mathematical Programming 25 (1983) 329–342.
- Y. Yamamoto and K. Murata, “A new variable dimension algorithm: extension for separable mappings, geometric interpretation and some applications”, Discussion Paper Series No. 129 (81-30), University of Tsukuba (Japan, 1981).
- A variable dimension fixed point algorithm and the orientation of simplices
Volume 30, Issue 3 , pp 301-312
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Fixed Point Algorithm
- System of Equations
- Orientation of Simplices
- Industry Sectors
- Author Affiliations
- 1. Institute of Socio-Economic Planning, University of Tsukuba, 305, Sakura, Ibaraki, Japan