<p>Accurate inverses and determinants of structured matrices have attracted increasing attention in the application areas of numerical linear algebra. <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({{ SDD}}_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi mathvariant="italic">SDD</mi> </mrow> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> matrices were introduced by Wang and Wang (AIMS Math 8:24999–25016, 2023). In this paper, a parametrization of an <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({ SDD}_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi mathvariant="italic">SDD</mi> </mrow> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> <i>Z</i>-matrix is investigated. Then the inverse and determinant of an <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\({ SDD}_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi mathvariant="italic">SDD</mi> </mrow> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> <i>Z</i>-matrix are computed to high relative accuracy under a weak assumption. <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\({ B}_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>B</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation>-matrices that extends <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\({ B}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>B</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-matrices are introduced and its determinants are also computed to high relative accuracy by using its parametrization. Numerical experiment indicates the accuracy of the inverse and determinant for the matrices.</p>