Rounding Errors in Algebraic Processes

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Courier Corporation, Jan 1, 1994 - Mathematics - 161 pages
Elementary introduction to problem of cumulative effect of rounding errors in a very large number of arithmetical calculations—particularly applicable to computer operations. Simple representative analyses illustrate techniques. Topics include fundamental arithmetic operations, computations involving polynomials and matrix computations. Results deal exclusively with digital computers but are equally applicable to desk calculators. Bibliography.
 

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Contents

THE FUND AMENTAL ARITH METI c o PERAT Ions
1
compUTATIONS INvolving PolyNoMIALs
34
Matrix computations
79
Accuracy of computed solution
102
Inversion of a general matrix
109
Triangular decomposition with partial pivoting
115
Iterative refinement of the solution
121
Assessment of a computed inverse
127
Sensitivity of the eigenvalues of a matrix
135
Calculation of the eigenvectors of a symmetric tridiagonal matrix
142
Calculation of fA using floatingpoint accumulation
149
Additional comments
155
index
159
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