By J. C. Nash
ISBN-10: 0852743181
ISBN-13: 9780852743188
Designed to aid humans clear up numerical difficulties on small desktops, this book's major topic parts are numerical linear algebra, functionality minimization and root-finding. This version has been revised and up to date, the most distinction being that the algorithms are offered in rapid Pascal.
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Extra resources for Compact numerical methods for computers: lin. algebra and function minimisation
Example text
9 ? 10 ? 11 ? 3.
0; for i := 1 to nRow do {STEP 5} begin x0 := W[i,j]; y0 := W[i,k]; p := p+x0*y0; q := q+x0*x0; r := r+y0*y0; end; Z[j] := q; Z[k] := r; {Now come important convergence test considerations. } if (q<=e2*2[1]) or (abs(p)<= tol*q) then RotCount := RotCount-1 {There is no more work on this particular pair of columns in the 37 38 Compact numerical methods for computers Algorithm 1. ) current sweep. That is, we now go to STEP 11. The first condition checks for very small column norms in BOTH columns, for which no rotation makes sense.
THE GIVENS’ REDUCTION The above approach to the computation of a singular-value decomposition and least-squares solution works very well on a small computer for relatively small matrices. For instance, it can handle least-squares regression calculations involving up to 15 economic time series with 25 years of data in less than 2000 words of main memory (where one matrix element occupies two words of storage). While such problems are fairly common in economics, biological and sociological phenomena are likely to have associated with them very large numbers of observations, m, even though the number of variables, n, may not be large.
Compact numerical methods for computers: lin. algebra and function minimisation by J. C. Nash
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