Lehmer

An \(n \times n\) Lehmer matrix is a symmetric positive-definite matrix whose upper-triangle is defined via the equation

\[A(i,j) = \frac{i+1}{j+1},\;\;\; i \le j.\]

The inverse of the Lehmer matrix is known to be symmetric tridiagonal (with positive eigenvalues), and the condition number is known to be bounded by the relationship

\[n \le \text{cond}(A) \le 4 n^2.\]

C++ API

void Lehmer(Matrix<F> &L, Int n)

void Lehmer(AbstractDistMatrix<F> &L, Int n)

C API

ElError ElLehmer_s(ElMatrix_s L, ElInt n)

ElError ElLehmer_d(ElMatrix_d L, ElInt n)

ElError ElLehmer_c(ElMatrix_c L, ElInt n)

ElError ElLehmer_z(ElMatrix_z L, ElInt n)

ElError ElLehmerDist_s(ElDistMatrix_s L, ElInt n)

ElError ElLehmerDist_d(ElDistMatrix_d L, ElInt n)

ElError ElLehmerDist_c(ElDistMatrix_c L, ElInt n)

ElError ElLehmerDist_z(ElDistMatrix_z L, ElInt n)

Python API

Lehmer(L, n)