Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
2007-11-13
2007-11-13
Malzahn, D. H. (Department: 2193)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
10447371
ABSTRACT:
One embodiment of the present invention provides a system that solves an overdetermined system of interval linear equations. During operation, the system receives a representation of the overdetermined system of interval linear equations Ax=b, wherein A is a matrix with m rows corresponding to m equations, and n columns corresponding to n variables, and wherein x includes n variable components, b includes m scalar components, and m>n. Next, the system performs a Gaussian Elimination operation to transform Ax=b into the form[TW]x=[uv],wherein T is a square upper triangular matrix of order n, u is a vector with n components, v is a vector with m−n components, and W is a matrix with m−n rows and n columns, wherein W is zero except in the last column, which is represented as a column vector z with m−n components. Next, the system performs an interval intersection operation based on the equations zixn=vi(i=1, . . . , m−n) and Tnnx=unto solve for xn. If xnis not the empty interval, the system performs a back substitution operation using xnand Tx=u to solve for the remaining components (xn−1, . . . , x1) of x.
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Hansen Eldon R.
Walster G. William
Malzahn D. H.
Park Vaughan & Fleming LLP
Sun Microsystems Inc.
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