6 problems

Let $(\mathcal{F}_{\mathbb{M}}^{\mathbb{M}},{\Greekmath 011A})$ be a Hilbert function space. Assume that $\mathcal{E}=\{e_i\}_{i\in I}\subset \mathcal{F}_{\mathbb{M}}^{\mathbb{M}}$…

Randomized-BCGS stability conjecture. The overall stability of the two-stage algorithm with randomized block classical Gram–Schmidt pre-processing is ensured when

Let $\mathcal{X}$ be the input matrix, let $\bar{Q}$ be the computed orthogonal factor produced by BCGSI+LS, let $u$ denote the working unit roundoff, and let $\mathcal{O}(u)$ deno…

Let $\{a_n\}_{n=1}^{\infty}$ be a sequence of distinct Clifford numbers in $B^{m+1}$, and let $T_{a_1,\ldots,a_n}$ be the functions obtained by the Gram–Schmidt orthogonalization p…

Let $f_k$ be the functions defined by … and let $(e_j)_{j\ge2}$ be the orthonormal sequence obtained from $(f_j)_{j\ge2}$ by the Gram–Schmidt process, with the normalization used i…

Let $A$ be the symmetric positive-definite matrix defining the non-standard inner product, let $Z$ be the input matrix with $m$ rows, let $n$ be the number of columns, and let…