# x31.txt # # Reference: # # Helmut Spaeth, # Mathematical Algorithms for Linear Regression, # Academic Press, 1991, # ISBN 0-12-656460-4. # # N L Schryer, # Certification of Algorithm 238: # Chebyshev Solution to an Overdetermined Linear System, # Collected Algorithms of the ACM. # # Discussion: # # A 10 by 3 linear system is considered, of the form # # There are 10 rows of data. Data includes: # # I, the index; # A1, column 1; # A2, column 2; # A3, column 3; # B, the right hand side. # # We seek a model of the form: # # B = A1 * X1 + A2 * X2 + A3 * X3 # # A solution is sought which minimizes the maximum absolute deviation. # # The correct solution is (-3,4,-1). # 5 columns 10 rows Index A1 A2 A3 B 1 11 -8 6 -68 2 0 -15 -12 -54 3 -13 -3 10 11 4 7 8 2 3 5 10 -7 9 -64 6 0 -5 5 -19 7 7 10 9 13 8 -15 0 15 30 9 -15 3 -15 72 10 2 5 14 -5