Scientific data analysis: an introduction to overdetermined systems
This monograph considers overdetermined systems, i.e., inconsistent systems with more equations than unknowns, in scientific data reduction. Although not a text on statistics, numerical methods, or matrix computations, all three enter into the discussion. The book is intended for the scientist or engineer who has gathered data that needs to be modelled by a mathematical system, perhaps linear or non-linear, and to be solved to obtain best estimates of various parameters. Programs and subroutines, mostly in FORTRAN, a few in BASIC, and one in C, illustrate many of the techniques presented.
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approximation arithmetic basic binary summation bit map bucket bytes calculate cascaded accumulators Chapter Cholesky decomposition chopping column order COND(A condition number convergence criterion decimal digits dimension discussion double-precision dynamic data structures efficient eigenvalue END DO END END IF END Eqns equations of condition Euclidean norm example exponent Fibonacci Figure fill-in floating-point floating-point numbers FORTRAN Gaussian elimination Givens transformation GOTO gradient hashing Householder transformation index array integer inverse iptr L2 norm large residuals least squares solution linear programming linear system linked list locations Lt solution machine epsilon mantissa mathematical matrix norm memory minimum multiplied n x n nonlinear nonzero elements normal equations NPL1 null objective function obtain operation count orthogonal matrix orthogonal transformations overdetermined system paired vectors pivot pointer positive simplex method single-precision singular values solving space sparse matrix stored subroutine total least squares transpose two-dimensional array TYPE unit matrix variable zero