In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.
The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix ...The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix and its mother matrix. Theoretical analysis and numerical evidence show that, fora class of row or column symmetric matrices, the QR factorization using the mother matrix rather than therow or column symmetric matrix per se can save dramatically the CPU time and memory without loss of anynumerical precision.展开更多
文摘In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.
基金This work was supported by the National Natural Science Foundation of China (Nos.60172026 & 60172005) the Basic Research Foundation of Tsinghua University (No. JC2001028)the Scientific Innovation Foundation of Ph.D. Candidates of Tsinghua Universit
文摘The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix and its mother matrix. Theoretical analysis and numerical evidence show that, fora class of row or column symmetric matrices, the QR factorization using the mother matrix rather than therow or column symmetric matrix per se can save dramatically the CPU time and memory without loss of anynumerical precision.
