Apparatus and method for inverting a 4×4 matrix

Details Apparatus and method for inverting a 4×4 matrix Apparatus and method for inverting a 4×4 matrix

2006-02-21

2006-02-21

Mai, Tan V. (Department: 2193)

Electrical computers: arithmetic processing and calculating

Electrical digital calculating computer

Particular function performed

Reexamination Certificate

active

07003542

ABSTRACT:
An apparatus and method for inverting a 4×4 source matrix. A source matrix is divided into four 2×2 sub-matrices. A plurality of sub-matrix products are subsequently calculated from the sub-matrices. Next, a determinant of the source matrix is calculated to form a determinant residue utilizing the previously computed sub-matrix products. Calculation of partial inverse for each sub-matrix is next performed, using the sub-matrix products and determinants of the sub-matrices. Finally, an inverse of each sub-matrix is calculated, utilizing the partial inverse sub-matrices and the determinant residue to form an inverse of the 4×4 source matrix. The article allows processors to store two floating-point elements within a Single Instruction Multiple Data (SIMD) register. Accordingly, a sub-matrix is represented using two SIMD registers, resulting in improved computational locality and efficiency. Other embodiments are described and claimed.

REFERENCES:
patent: 5557511 (1996-09-01), Bayard
patent: 6748098 (2004-06-01), Rosenfeld

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