rcond                 package:Matrix                 R Documentation

_E_s_t_i_m_a_t_e _t_h_e _R_e_c_i_p_r_o_c_a_l _C_o_n_d_i_t_i_o_n _N_u_m_b_e_r

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

     Estimate the reciprocal of the condition number of a matrix.

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

     rcond(x, ...)

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

       x: a matrix. No missing values or IEEE special values are
          allowed. 

     ...: further arguments passed to or from other methods.

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

     An estimate of the reciprocal condition number of 'x'.

_B_A_C_K_G_R_O_U_N_D:

     The condition number of a matrix is the product of the matrix and
     the norm of its inverse (or pseudo-inverse if the matrix is not
     square). Since it can take on values between 1 and infinity,
     inclusive, it can be viewed as a measure of how close a matrix is
     to being rank deficient. It can also be viewed as a factor by
     which errors in solving linear systems with this matrix as
     coefficient matrix could be magnified.

     Condition numbers are usually estimated, since exact computation
     is costly in terms of floating-point operations. An (over)
     estimate of reciprocal condition number is given, since by doing
     so overflow is avoided. Matrices are well-conditioned if the
     reciprocal condition number is near 1 and ill-conditioned if it is
     near zero.

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

     Golub, G., and Van Loan, C. F. (1989). _Matrix Computations,_ 2nd
     edition, Johns Hopkins, Baltimore.

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

     x <- Matrix(rnorm(9), 3, 3)
     rcond(x)
     rcond(hilbert(9))  # should be about 9.1e-13
     h9 <- hilbert(9)
     class(h9) <- Matrix.class(h9)  # now Hermitian
     rcond(h9) # slightly different answer - different algorithm

