Numerical Methods, Software, and AnalysisMathematics and computer science background. Numerical software. Errors, roud-off, and stabilitly. Models and formulas for numerical computations. Interpolation. Matrices and linear equations. Differentiation and integration. Nonlinear equations. Ordinary differential equations. Partial differential equations. Approximation of functions and data. Software practice, costs, and engineering. Software performance evaluation. The validation of numerical computations. Protran. |
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Page 360
... least - squares approximation is less than twice that of the best Chebyshev approximation . 2. If the random errors are " well - behaved , " then the least - squares ... Least Squares and Regression A Formulation of least-squares problems.
... least - squares approximation is less than twice that of the best Chebyshev approximation . 2. If the random errors are " well - behaved , " then the least - squares ... Least Squares and Regression A Formulation of least-squares problems.
Page 368
... least - squares software of Lawson - Hanson discussed later . An estimate of the work for the orthogonal factorization method yields about M'N - M3 / 3 operations ( one add + one multiply ) . If N is about the same size as M , then this ...
... least - squares software of Lawson - Hanson discussed later . An estimate of the work for the orthogonal factorization method yields about M'N - M3 / 3 operations ( one add + one multiply ) . If N is about the same size as M , then this ...
Page 369
... least - squares approximation F ( a * , t ) is ( B ) Suppose p discrete set x ; = = = 0 , q = s 4 , and r = 1. Replace the interval [ 0 , 5 ] by the ( i - 1 ) / 20 for i = 1 , 2 ... least - squares LEAST SQUARES AND REGRESSION 369.
... least - squares approximation F ( a * , t ) is ( B ) Suppose p discrete set x ; = = = 0 , q = s 4 , and r = 1. Replace the interval [ 0 , 5 ] by the ( i - 1 ) / 20 for i = 1 , 2 ... least - squares LEAST SQUARES AND REGRESSION 369.
Contents
Core Material | 4 |
PARTIAL DIFFERENTIAL EQUATIONS | 10 |
CHAPTER | 15 |
Copyright | |
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accuracy Algorithm analysis Apply approach approximation assume basis functions boundary calculation CALL choose coefficients Compare complex computation Consider continuous convergence correct cubic data set defined depends derivatives difference difficult digits discretization discussed domain effect efficiency elements elimination error estimate evaluations example factor Figure finite formula Fortran four functions Gauss given gives Hermite IMSL increases initial integration interpolation interval iteration knots language least-squares less linear linear system lines mathematical matrix method needed nonlinear norm normal Note obtain parameters partial differential equation performance points polynomial PRINT problem produce PROTRAN random range REAL representations root round-off rule side simple smooth solution solve space specific spline squares standard statement step Table Theorem usually values variables vector Write zero