Polynomial2              package:assist              R Documentation

_C_a_l_c_u_l_a_t_e _R_e_p_r_o_d_u_c_i_n_g _K_e_r_n_e_l_s _f_o_r _P_o_l_y_n_o_m_i_a_l _S_p_l_i_n_e_s _o_n [_0, _T]

_D_e_s_c_r_i_p_t_i_o_n:

     Return a matrix evaluating reproducing kernels for polynomial
     splines at observed points.

_U_s_a_g_e:

     linear2(s, t=s)
     cubic2(s, t=s)
     quintic2(s, t=s)
     septic2(s, t=s)

_A_r_g_u_m_e_n_t_s:

       s: a vector of non-negative values, at which the kernels are
          evaluated. 

       t: an optional non-negative vector. Default is the same as s. 

_D_e_t_a_i_l_s:

     The reproducing kernels implemented in these functions are based
     on Green functions. The domain is [0, T], where T is a given
     positive number.

_V_a_l_u_e:

     a matrix with the numbers of row and column equal to the length of
     s and t respectively. The [i, j] element is the reproducing kernel
     of linear, cubic, quintic, or septic spline  evaluated at (s[i],
     t[j]).

_A_u_t_h_o_r(_s):

     Chunlei Ke chunlei_ke@pstat.ucsb.edu and Yuedong Wang
     yuedong@pstat.ucsb.edu

_R_e_f_e_r_e_n_c_e_s:

     Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol.
     59.

_S_e_e _A_l_s_o:

     'ssr', 'linear', 'cubic',  'quintic', 'septic'

_E_x_a_m_p_l_e_s:

     x<- seq(0, 5, len=10)
     linear2(x)

