Haw-ren Fang

A Retrograde Approximation Algorithm for Two-Player Can’t Stop (2008)

James Glenn, Haw-ren Fang, Clyde P. Kruskal

Abstract. A two-player, finite, probabilistic game with perfect information can be presented as a four-partite graph. For Can’t Stop, the graph is cyclic and the challenge is to determine the...

Farthest Centroids Divisive Clustering ∗ (2008)

Haw-ren Fang, Yousef Saad

A method is presented to partition a given set of data entries embedded in Euclidean space by recursively bisecting clusters into smaller ones. The initial set is subdivided into two subsets whose...

Fast Approximate kNN Graph Construction for High Dimensional Data via Recursive Lanczos Bisection ∗ (2008)

Jie Chen, Haw-ren Fang, Yousef Saad

Nearest neighbor graphs are widely used in data mining and machine learning. The brute-force method to compute the exact kNN graph takes Θ(dn 2) time for n data points in the d dimensional Euclidean...

Two Classes of Multisecant Methods for Nonlinear Acceleration ∗ (2007)

Haw-ren Fang, Yousef Saad

Many applications in science and engineering lead to models which require solving large-scale fixed point problems, or equivalently, systems of nonlinear equations. Several successful techniques for...

Analysis of Block LDL^T Factorizations for Symmetric Indefinite Matrices (2007)

Haw-ren Fang

We consider the block LDL^T factorizations for symmetric indefinite matrices in the form LBL^T, where L is unit lower triangular and B is block diagonal with each diagonal block having dimension 1 or...

Modified Cholesky Algorithms: A Catalog with New Approaches (2006)

Fang, Haw-ren, O'Leary, Dianne P.

Given an $n \times n$ symmetric possibly indefinite matrix $A$, a modified Cholesky algorithm computes a factorization of the positive definite matrix $A+E$, where $E$ is a correction matrix. Since...

Modified Cholesky Algorithms: A Catalog with New Approaches (2006)

Fang, Haw-ren, O'Leary, Dianne P.

Given an $n \times n$ symmetric possibly indefinite matrix $A$, a modified Cholesky algorithm computes a factorization of the positive definite matrix $A+E$, where $E$ is a correction matrix. Since...

Matrix Factorizations, Triadic Matrices, and Modified Cholesky Factorizations for Optimization (2006)

Fang, Haw-ren

This thesis focuses on the Cholesky-related factorizations of symmetric matrices and their application to Newton-type optimization. A matrix is called triadic if it has at most two nonzero...

Matrix Factorizations, Triadic Matrices, and Modified Cholesky Factorizations for Optimization (2006)

Fang, Haw-ren

This thesis focuses on the Cholesky-related factorizations of symmetric matrices and their application to Newton-type optimization. A matrix is called triadic if it has at most two nonzero...

The Nature of Retrograde Analysis for Chinese Chess (2006)

Fang, Haw-ren

Retrograde analysis has been successfully applied to solve Awari and construct 6-piece Western chess endgame databases. However, its application to Chinese chess is limited because of the special...

Stable Factorizations of Symmetric Tridiagonal and Triadic Matrices (2006)

Fang, Haw-ren, O'Leary, Dianne

We call a matrix triadic if it has no more than two nonzero off-diagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider $LXL^T$ factorizations of...

Backward Error Analysis of Factorization Algorithms for Symmetric and Symmetric Triadic Matrices (2006)

Fang, Haw-ren

We consider the $LBL^T$ factorization of a symmetric matrix where $L$ is unit lower triangular and $B$ is block diagonal with diagonal blocks of order $1$ or $2$. This is a generalization of the...

The Nature of Retrograde Analysis for Chinese Chess (2006)

Fang, Haw-ren

Retrograde analysis has been successfully applied to solve Awari and construct 6-piece Western chess endgame databases. However, its application to Chinese chess is limited because of the special...

Stable Factorizations of Symmetric Tridiagonal and Triadic Matrices (2006)

Fang, Haw-ren, O'Leary, Dianne

We call a matrix triadic if it has no more than two nonzero off-diagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider $LXL^T$ factorizations of...

Backward Error Analysis of Factorization Algorithms for Symmetric and Symmetric Triadic Matrices (2006)

Fang, Haw-ren

We consider the $LBL^T$ factorization of a symmetric matrix where $L$ is unit lower triangular and $B$ is block diagonal with diagonal blocks of order $1$ or $2$. This is a generalization of the...

Modified Cholesky Algorithms: A Catalog with New Approaches (2006)

Haw-ren Fang, Dianne P. O’leary

Given an n × n symmetric possibly indefinite matrix A, a modified Cholesky algorithm computes a factorization of the positive definite matrix A+E, where E is a correction matrix. Since the...

Stable factorizations of symmetric tridiagonal and triadic matrices (2006)

Haw-ren Fang

Abstract. We call a matrix triadic if it has no more than two nonzero off-diagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider LXL T...

A retrograde approximate algorithm for one-player can’t stop (2006)

James Glenn, Haw-ren Fang, Clyde P. Kruskal

Abstract. A one-player, finite, probabilistic game with perfect information can be presented as a bipartite graph. For one-player Can’t Stop, the graph is cyclic and the challenge is to determine...