documentclass{article}

usepackage{booktabs,array}

begin{document}

begin{table}
  centering
  caption{A table caption}
  begin{tabular}{@{}>{hspace{3em}}p{.8linewidth}@{}}
    toprule
    unskip Initialization: This is where the pseudocode initialization is supposed to go.
    It may span several lines within the texttt{tabular}. \
    textbf{Error nonlinearity update:} Some content \[.25normalbaselineskip]
    centeringarraybackslash
    $setlength{arraycolsep}{0pt}
      begin{array}{r>{{}}l}
        f(x) &= ax^2 + bx + c \
        g(x) &= f(x) \
        h(x) &= displaystyle frac{a}{e}
      end{array}$ \
    textbf{Incremental update:} Some content \
    qquad $f(x) = ax^2 + bx + c$ \
    textbf{Diffusion update:} Some content \
    qquad $g(x) = f(x)$ \
    textbf{Decision:} Some content \
    qquad $h(x) = frac{a}{e}$ \
    bottomrule
  end{tabular}
end{table}

end{document}