An efficient implementation of a conformal mapping method based on the Szego¨ kernel
SIAM Journal on Numerical Analysis
Fast parallel algorithms for QR and triangular factorization
SIAM Journal on Scientific and Statistical Computing
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
A matrix problem with application to rapid solution of integral equations
SIAM Journal on Scientific and Statistical Computing
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Fast algorithms with preprocessing for matrix-vector multiplication problems
Journal of Complexity
Fast Gaussian elimination with partial pivoting for matrices with displacement structure
Mathematics of Computation
Matrix computations (3rd ed.)
A displacement approach to efficient decoding of algebraic-geometric codes
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Nearly optimal computations with structured matrices
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Fast reliable algorithms for matrices with structure
Fast reliable algorithms for matrices with structure
Transformations of Cauchy Matrices, Trummer's Problem and a Cauchy-Like Linear Solver
IRREGULAR '98 Proceedings of the 5th International Symposium on Solving Irregularly Structured Problems in Parallel
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Fast algorithms for multivariable systems.
Fast algorithms for multivariable systems.
An efficient solution for Cauchy-likesystems of linear equations
Computers & Mathematics with Applications
Hi-index | 0.00 |
Let Z be a set of integers and Z n×n be a ring for any integer n. We define ${\hat{s}}\in \mathbf{Z}^{n}$ as a latter point. Hom(Z n ,Z m ) denotes as a homomorphism of Z n into Z m . For any element ${\hat{q}}$ in Z n , we define S+T:Z n →Z m as $(S+T)({\hat{q}})=S({\hat{q}})+T({\hat{q}})$ . As a result, S+T become a homomorphism of Z n into Z m . We also define kU:Z n →Z m as $(kU)({\hat{q}})=k(U({\hat{q}}))$ . Consequently, kU become a homomorphism of Z n into Z m . Moreover, Hom (Z n ,Z m ) is isomorphic to Z n×m . A novel class of the structured matrices which is a set of elements of Hom (Z n ,Z n ) over a ring of integers with a displacement structure, referred to as a C-Cauchy-like matrix, will be formulated and presented. Using the displacement approach, which was originally discovered by Kailath, Kung, and Morf (J. Math. Anal. Appl. 68:395–407, 1979), a new superfast algorithm for the multiplication of a C-Cauchy-like matrix of the size n×n over a field with a vector will be designed. The memory space for storing a C-Cauchy-like matrix of the size n×n over a field is O(n) versus O(n 2) for a general matrix of the size n×n over a field. The arithmetic operations of a product of a C-Cauchy-like matrix and a vector is reduced dramatically to O(n) from O(n 2), which can be used to transform a latter point ${\hat{s}}\in Z^{n}$ to another latter point ${\hat{t}}\in Z^{n}$ such that ${\hat{t}}=C{\hat{s}}$ . Moreover, the displacement structure can also be extended to a Kronecker matrix W ⊗ Z. A new class of the Kronecker-like matrices with the displacement rank r, r