GPGPU Programming for Games and Science

356 GPGPU Programming for Games and Science

minimum of F occurs at the vertex. The gradient equation leads to a system

of two linear equations in the unknowns A and B,namely,(0, 0) = ∇F =

2



n

i=0

[(Ax

i

+ B − y

i

](x

i

, 1). The linear system is listed next, where we use

the statistical concept of expected value of a uniformly distributed random

variable U,namely,E[U ]=(



n

i=0

u

i

)/n;



E[X

2

] E[X]

E[X]1



A

B



=



E[XY ]

E[Y ]



(7.3)

The solution to this system provides the coefficients for the least squares fit.



A

B



=

1

E[X

2

] −E[X]

2



E[XY ] −E[X]E[Y ]

E[X

2

]E[Y ] − E[XY ]E[X]



(7.4)

Although the construction is mathematically correct, in practice when us-

ing floating-point num