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- Jesse L. Barlow, Udaya B. Vemulapati
- PPSC
- 1989

- Jesse Barlow, Jam Es, D Em M El E T
- 1990

n fi When com puting eigenvalu es of sym m etric m atrices an d singular valu es of general m atrices i nite precision arithmetic we in general only expect to compute them with an error bound pro-n portional to the product of mach ine precision an d the norm of the matrix. In particular, we do ot expect to com pute tiny eigenvalu es an d singular valu es to… (More)

- Haoying Fu, Michael K. Ng, Mila Nikolova, Jesse L. Barlow
- SIAM J. Scientific Computing
- 2006

- Xin Yang, Haoying Fu, Hongyuan Zha, Jesse L. Barlow
- ICML
- 2006

The problem of nonlinear dimensionality reduction is considered. We focus on problems where prior information is available, namely, semi-supervised dimensionality reduction. It is shown that basic nonlinear dimensionality reduction algorithms, such as Locally Linear Embedding (LLE), Isometric feature mapping (ISOMAP), and Local Tangent Space Alignment… (More)

- Szu-Min Lu, Jesse L. Barlow
- SIAM J. Matrix Analysis Applications
- 1996

This paper studies the solution of the linear least squares problem for a large and sparse m by n matrix A with m n by QR factorization of A and transformation of the right-hand side vector b to Q T b. A multifrontal-based method for computing Q T b using Householder factorization is presented. A theoretical operation count for the K by K unbordered grid… (More)

- Nela Bosner, Jesse L. Barlow
- SIAM J. Matrix Analysis Applications
- 2007

Two new algorithms for one-sided bidiagonalization are presented. The first is a block version which improves execution time by improving cache utilization from the use of BLAS 2.5 operations and more BLAS 3 operations. The second is adapted to parallel computation. When incorporated into singular value decomposition software, the second algorithm is faster… (More)

- Jesse L. Barlow, Ivan Slapni
- 1993

There is now a large literature on structured perturbation bounds for eigen-value problems of the form Hx = Mx; where H and M are Hermitian. These results give relative error bounds on the ith eigenvalue, i, of the form 2 and bound the error in the ith eigenvector in terms of the relative gap, min j6 =i ji ? jj jijj 1=2 : In general, this theory usually… (More)

- Geunseop Lee, Haoying Fu, Jesse L. Barlow
- SIAM J. Scientific Computing
- 2013

- Jesse L. Barlow, Erwin H. Bareiss
- Computing
- 1985

- Alicja Smoktunowicz, Jesse L. Barlow, Julien Langou
- Numerische Mathematik
- 2006

An error analysis result is given for classical Gram–Schmidt fac-torization of a full rank matrix A into A = QR where Q is left orthogonal (has orthonormal columns) and R is upper triangular. The work presented here shows that the computed R satisfies R T R = A T A + E where E is an appropriately small backward error, but only if the diagonals of R are… (More)