LAPACKstyle codes for pivoted Cholesky and QR updating

was supported by an EPSRC Research Studentship. Abstract. Routines exist in LAPACK for computing the Cholesky fac-torization of a symmetric positive definite matrix and in LINPACK there is a pivoted routine for positive semidefinite matrices. We present new higher level BLAS LAPACK-style codes for computing this pivoted fac-torization. We show that these can be many times faster than the LIN-PACK code. Also, with a new stopping criterion, there is more reliable rank detection and smaller normwise backward error. We also present algorithms that update the QR factorization of a matrix after it has had a block of rows or columns added or a block of columns deleted. This is achieved by updating the factors Q and R of the original matrix. We present some LAPACK-style codes and show these can be much faster than computing the factorization from scratch. 1 Pivoted Cholesky Factorization 1.