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[CT097]

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
Type : Contributed Talk
Abstract : Premature convergence of the seed system can lead to shifted systems being unsolved when applying shifted Krylov subspace methods to solve shifted linear systems. To avoid this, a seed-switching technique may be a method of choice; however, the conventional product-type methods cannot use this technique since it requires the collinear residuals between the seed and shifted systems. We propose a variant of the shifted BiCGStab method so that the technique can be applied.
Classification : 65Fxx
Format : Talk at Waseda University
Author(s) :
- Ren-Jie Zhao (Nagoya University)
- Tomohiro Sogabe (Nagoya University)
- Tomoya Kemmochi (Nagoya University)
- Shao-Liang Zhang (Nagoya University)

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
Type : Contributed Talk
Abstract : In 2010, Vandereycken and Vandewalle proposed a preconditioner for the Riemannian trust-region (RTR) method on the manifold of symmetric positive semidefinite matrices of fixed rank. Here, we generalize their work to the manifold of fixed-rank matrices. We use the RTR method with our preconditioner to solve a stiff time-dependent PDE, the Allen--Cahn equation, on the manifold of fixed-rank matrices. Numerical experiments show the efficiency of our preconditioner. This is joint work with Bart Vandereycken.
Classification : 65F55, 65F45, 65F08, 65L04, 65L05
Format : Talk at Waseda University
Author(s) :
- Marco Sutti (National Center for Theoretical Sciences, Mathematics Division, Taipei, Taiwan)

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
Type : Contributed Talk
Abstract : I'll discuss a new class of nested Hierarchical matrices in $2$D (HODLR2D^2). This is based on weak admissibility criteria and the compressions are done using NCA. Using this Hierarchical framework, one can perform matrix-vector product that scales almost linearly; hence, large dense linear systems arising out of $N$ body problems can be solved using iterative solvers with almost linear complexity. Also, I'll discuss its performance over other Hierarchical matrices and applications in solving integral equation and radial basis interpolation.
Classification : 65F55, 65R20, 65R10, Numerical Linear Algebra
Format : Talk at Waseda University
Author(s) :
- Ritesh Khan (Indian Institute of Technology Madras)
- Sivaram Ambikasaran (Indian Institute of Technology Madras)

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
Type : Contributed Talk
Abstract : We extend our prior work on Monte Carlo algorithms for solving large linear systems to compute other matrix functions such as exponential and logarithm. Our recent algorithm that computes with matrix tiles is shown to guarantee convergence for sufficiently large tiles. We compute matrix functions by summing a polynomial approximation (e.g. Taylor, Chebyshev). We investigate the convergence conditions for each function and optimize the algorithm by adjusting the parameters.
Classification : 65F60, 65C05
Format : Talk at Waseda University
Author(s) :
- Hyeji Choi (Stony Brook University)

Session Time & Room : 5B (Aug.25, 10:40-12:20) @E603
Type : Contributed Talk
Abstract : One of the more recent technological advancements is assistive robots, which can improve patient-centered care in the health sector. This paper presents a unique set of continuous nonlinear control laws derived from a Lyapunov-based control scheme for navigation of an assistive robot and a rehabilitation wheelchair robot together modeled as a new autonomous robotic dog and rehabilitation wheelchair system. The computer simulations also present a qualitative analysis of the effectiveness of the control laws.
Classification : 70B15, 93C85, 93D05, 93C10
Author(s) :
- Bibhya Nand Sharma (The University of the South Pacific )
- Sandeep Kumar (The University of the South Pacific )