Index 977 Hyperbolic partial differential equations 827 Inheritance 7 advective equation 835 Initial value problems 708,827f. flux-conservative initial value problems see also Differential equations; 834ff Partial differential equations Hypergeometric function 208ff.,271ff. Injection operator 873 routine for 272f. Instability see Stability Hypothesis,null 609 Integer programming 443 Integral equations 788ff. adaptive stepsize control 797 BM xvii block-by-block method 797 bad random number generator 277 correspondence with linear algebraic equa- PC3,285,303,894 tions 788ff. radix base for floating point arithmetic degenerate kernel 794 483 eigenvalue problems 789,794 IBM checksum 901f. error estimate in solution 793 ICCG (incomplete Cholesky conjugate gradient Fredholm 788f..791f. method)833 Fredholm alternative 789 ICF (intrinsic correlation function)model 826 homogeneous,second kind 793f. Identity (unit)matrix 34 ill-conditioned 789 IEEE floating point format 285,890f. infinite range 797f. if structure 11 inverse problems 789,804ff. warning about nesting 11 kernel 788f. IIR (infinite impulse response)filter 559,573 nonlinear 790,796 Ill-conditioned integral equations 789 Nystrom method 791f..797 Image processing 525,812 product Nystrom method 797 cosine transform 519 with singularities 797ff. fast Fourier transform(FFT)525,530, with singularities.worked example 801 812 subtraction of singularity 798 as an inverse problem 812 symmetric kernel 794 maximum entropy method (MEM)818ff. unstable quadrature 796 from modulus of Fourier transform 814 Volterra 789f,794f. wavelet transform 603 wavelets 791 imatrix()utility 944 see also Inverse problems Implicit Integral operator,wavelet approximation of conversion of data types 24f.,930 603f.791 function theorem 347 Integration of functions 129ff. pivoting 38 cosine integrals 257 shifts in QL method 478ff. Fourier integrals 584f Implicit differencing 836 Fourier integrals,infinite range 590f. for diffusion equation 848 Fresnel integrals 255 for stiff equations 735f.,749 Gauss-Hermite 153 Importance sampling,in Monte Carlo 316f. Gauss-Jacobi 154 Improper integrals 141ff. Gauss-Laguerre 152 Impulse response function 538,549,559 Gauss-Legendre 151 IMSL xvii.35,72,212.371,376,461 integrals that are elliptic integrals 261 In-place selection 342 path integration 208ff. Include files 17,930 sine integrals 257 Incomplete beta function 226ff. see also Quadrature for F-test 619 Integro-differential equations 791 routine for 227f. Interface,in programs 7 for Student's t 616.618 Intermediate value theorem 350 Incomplete Cholesky conjugate gradient method Internet xvii (ICCG)833 Interpolation 105ff. Incomplete gamma function 216 Aitken's algorithm 108 for chi-square 621,660,663f. avoid 2-stage method 106 deviates from 290ff. avoid in Fourier analysis 576 in mode estimation 616 bicubic 125f. routine for 218f. bilinear 123f Increment of linear congruential generator caution on high-order 106f. 276 coefficients of polynomial 106,120ff.. Indentation of blocks 11 197,582 Index 965ff. for computing Fourier integrals 586 this entry 977 error estimates for 106 Index table 329,338 of functions with poles 111ff. Inequality constraints 431 inverse quadratic 360,402ff.Index 977 Hyperbolic partial differential equations 827 advective equation 835 flux-conservative initial value problems 834ff. Hypergeometric function 208ff., 271ff. routine for 272f. Hypothesis, null 609 IBM xvii bad random number generator 277 PC 3, 285, 303, 894 radix base for floating point arithmetic 483 IBM checksum 901f. ICCG (incomplete Cholesky conjugate gradient method) 833 ICF (intrinsic correlation function) model 826 Identity (unit) matrix 34 IEEE floating point format 285, 890f. if structure 11 warning about nesting 11 IIR (infinite impulse response) filter 559, 573 Ill-conditioned integral equations 789 Image processing 525, 812 cosine transform 519 fast Fourier transform (FFT) 525, 530, 812 as an inverse problem 812 maximum entropy method (MEM) 818ff. from modulus of Fourier transform 814 wavelet transform 603 imatrix() utility 944 Implicit conversion of data types 24f., 930 function theorem 347 pivoting 38 shifts in QL method 478ff. Implicit differencing 836 for diffusion equation 848 for stiff equations 735f., 749 Importance sampling, in Monte Carlo 316f. Improper integrals 141ff. Impulse response function 538, 549, 559 IMSL xvii, 35, 72, 212, 371, 376, 461 In-place selection 342 Include files 17, 930 Incomplete beta function 226ff. for F-test 619 routine for 227f. for Student’s t 616, 618 Incomplete Cholesky conjugate gradient method (ICCG) 833 Incomplete gamma function 216 for chi-square 621, 660, 663f. deviates from 290ff. in mode estimation 616 routine for 218f. Increment of linear congruential generator 276 Indentation of blocks 11 Index 965ff. this entry 977 Index table 329, 338 Inequality constraints 431 Inheritance 7 Initial value problems 708, 827f. see also Differential equations; Partial differential equations Injection operator 873 Instability see Stability Integer programming 443 Integral equations 788ff. adaptive stepsize control 797 block-by-block method 797 correspondence with linear algebraic equa￾tions 788ff. degenerate kernel 794 eigenvalue problems 789, 794 error estimate in solution 793 Fredholm 788f., 791f. Fredholm alternative 789 homogeneous, second kind 793f. ill-conditioned 789 infinite range 797f. inverse problems 789, 804ff. kernel 788f. nonlinear 790, 796 Nystrom method 791f., 797 product Nystrom method 797 with singularities 797ff. with singularities, worked example 801 subtraction of singularity 798 symmetric kernel 794 unstable quadrature 796 Volterra 789f., 794f. wavelets 791 see also Inverse problems Integral operator, wavelet approximation of 603f., 791 Integration of functions 129ff. cosine integrals 257 Fourier integrals 584ff. Fourier integrals, infinite range 590f. Fresnel integrals 255 Gauss-Hermite 153 Gauss-Jacobi 154 Gauss-Laguerre 152 Gauss-Legendre 151 integrals that are elliptic integrals 261 path integration 208ff. sine integrals 257 see also Quadrature Integro-differential equations 791 Interface, in programs 7 Intermediate value theorem 350 Internet xvii Interpolation 105ff. Aitken’s algorithm 108 avoid 2-stage method 106 avoid in Fourier analysis 576 bicubic 125f. bilinear 123f. caution on high-order 106f. coefficients of polynomial 106, 120ff., 197, 582 for computing Fourier integrals 586 error estimates for 106 of functions with poles 111ff. inverse quadratic 360, 402ff