The patent badge is an abbreviated version of the USPTO patent document. The patent badge does contain a link to the full patent document.
The patent badge is an abbreviated version of the USPTO patent document. The patent badge covers the following: Patent number, Date patent was issued, Date patent was filed, Title of the patent, Applicant, Inventor, Assignee, Attorney firm, Primary examiner, Assistant examiner, CPCs, and Abstract. The patent badge does contain a link to the full patent document (in Adobe Acrobat format, aka pdf). To download or print any patent click here.
Patent No.:
Date of Patent:
Nov. 18, 2008
Filed:
May. 14, 2007
Vance Faber, Carnation, WA (US);
Randall L. Dougherty, Seattle, WA (US);
Vance Faber, Carnation, WA (US);
Randall L. Dougherty, Seattle, WA (US);
LizardTech, Inc., Seattle, WA (US);
Abstract
A method of generating matrix factors for a finite-dimensional linear transform using a computer. The linear transform is represented by data values stored in a linear transformation matrix having a nonzero determinant. In one aspect, a first LU-decomposition is applied to the linear transformation matrix. Four matrices are generated from the LU-decomposition, including a first permutation matrix, a second permutation matrix, a lower triangular matrix having a unit diagonal, and a first upper triangular matrix. Additional elements include a third matrix Â, a signed permutation matrix Π such that A=ΠÂ, a permuted linear transformation matrix A', a second upper triangular matrix U, wherein the second upper triangular matrix satisfies the relationship Â=UA′. The permuted linear transformation matrix is factored into a product including a lower triangular matrix L and an upper triangular matrix U. The linear transformation matrix is expressed as a product of the matrix factors.