  We analyze the ground-state energy, local spin correlation, impurity spin
polarization, impurity-induced magnetization, and corresponding zero-field
susceptibilities of the symmetric single-impurity Kondo model on a
tight-binding chain with bandwidth $W=2{\cal D}$ and coupling strength $J_{\rm
K}$. We compare perturbative results and variational upper bounds from Yosida,
Gutzwiller, and first-order Lanczos wave functions to the numerically exact
data obtained from the Density-Matrix Renormalization Group (DMRG) and from the
Numerical Renormalization Group (NRG) methods. The Gutzwiller variational
approach becomes exact in the strong-coupling limit and reproduces the
ground-state properties from DMRG and NRG for large couplings. We calculate the
impurity spin polarization and its susceptibility in the presence of magnetic
fields that are applied globally/locally to the impurity spin. The Yosida wave
function provides qualitatively correct results in the weak-coupling limit. In
DMRG, chains with about $10^3$ sites are large enough to describe the
susceptibilities down to $J_{\rm K}/{\cal D}\approx 0.5$. For smaller Kondo
couplings, only the NRG provides reliable results for a general host-electron
density of states $\rho_0(\epsilon)$. To compare with results from Bethe
Ansatz, we study the impurity-induced magnetization and zero-field
susceptibility. For small Kondo couplings, the zero-field susceptibilities at
zero temperature approach $\chi_0(J_{\rm K}\ll {\cal D})/(g\mu_{\rm
B})^2\approx \exp[1/(\rho_0(0)J_{\rm K})]/(2C{\cal D}\sqrt{\pi e
\rho_0(0)J_{\rm K}})$, where $\ln(C)$ is the regularized first inverse moment
of the density of states. Using NRG, we determine the universal sub-leading
corrections up to second order in $\rho_0(0)J_{\rm K}$.
