Index to NUMAL Manual and Code Files

The Stichting Mathematisch Centrum at Amsterdam has granted permission to incorporate the complete NUMAL library manual into this CDROM. It may be freely used. It may be copied, provided that the name NUMAL and the attribution to the Stichting Mathematisch Centrum at Amsterdam are retained.

NUMAL in Historical Context by Jan Kok (April, 1996)

Introduction to NUMAL by P.W. Hemker (4th Revision, 1980)

1. Elementary Procedures

1.1. Real Vect and Mat Operations

1.1.1. Initialization

INIVEC (Code 31010, NOV/81)
INIMAT (Code 31011, NOV/81)
INIMATD (Code 31012, NOV/81)
INISYMD (Code 31013, NOV/81)
INISYMROW (Code 31014, NOV/81)

1.1.2. Duplication

DUPVEC (Code 31030, NOV/81)
DUPVECROW (Code 31031, NOV/81)
DUPROWVEC (Code 31032, NOV/81)
DUPVECCOL (Code 31033, NOV/81)
DUPCOLVEC (Code 31034, NOV/81)
DUPMAT (Code 31035, NOV/81)

1.1.3. Multiplication

MULVEC (Code 31020, NOV/81)
MULROW (Code 31021, NOV/81)
MULCOL (Code 31022, NOV/81)
COLCST (Code 31131, NOV/81)
ROWCST (Code 31132, NOV/81)

1.1.4. Scalar Products

1.1.4.1. Vector Vector Products

VECVEC (Code 34010, NOV/81)
MATVEC (Code 34011, NOV/81)
TAMVEC (Code 34012, NOV/81)
MATMAT (Code 34013, NOV/81)
TAMMAT (Code 34014, NOV/81)
MATTAM (Code 34015, NOV/81)
SEQVEC (Code 34016, NOV/81)
SCAPRD1 (Code 34017, NOV/81)
SYMMATVEC (Code 34018, NOV/81)

1.1.4.2. Matrix Vector Products

FULMATVEC (Code 31500, NOV/81)
FULTAMVEC (Code 31501, NOV/81)
FULSYMMATVEC (Code 31502, NOV/81)
RESVEC (Code 31503, NOV/81)
SYMRESVEC (Code 31504, NOV/81)

1.1.4.3. Matrix Matrix Products

HSHVECMAT (Code 31070, NOV/81)
HSHCOLMAT (Code 31071, NOV/81)
HSHROWMAT (Code 31072, NOV/81)
HSHVECTAM (Code 31073, NOV/81)
HSHCOLTAM (Code 31074, NOV/81)
HSHROWTAM (Code 31075, NOV/81)

1.1.5. Elimination

ELMVEC (Code 34020, NOV/81)
ELMCOL (Code 34023, NOV/81)
ELMROW (Code 34024, NOV/81)
ELMVECCOL (Code 34021, NOV/81)
ELMCOLVEC (Code 34022, NOV/81)
ELMVECROW (Code 34026, NOV/81)
ELMROWVEC (Code 34027, NOV/81)
ELMCOLROW (Code 34029, NOV/81)
ELMROWCOL (Code 34028, NOV/81)
MAXELMROW (Code 34025, NOV/81)

1.1.6. Interchanging

ICHVEC (Code 34030, NOV/81)
ICHCOL (Code 34031, NOV/81)
ICHROW (Code 34032, NOV/81)
ICHROWCOL (Code 34033, NOV/81)
ICHSEQVEC (Code 34034, NOV/81)
ICHSEQ (Code 34035, NOV/81)

1.1.7. Rotation

ROTCOL (Code 34040, NOV/81)
ROTROW (Code 34041, NOV/81)

1.1.8. Norms

INFNRMVEC (Code 31061, NOV/81)
INFNRMROW (Code 31062, NOV/81)
INFNRMCOL (Code 31063, NOV/81)
INFNRMMAT (Code 31064, NOV/81)
ONENRMVEC (Code 31065, NOV/81)
ONENRMROW (Code 31066, NOV/81)
ONENRMCOL (Code 31067, NOV/81)
ONENRMMAT (Code 31068, NOV/81)
ABSMAXMAT (Code 31069, NOV/81)

1.1.9. Scaling

REASCL (Code 34183, NOV/81)

1.2. Compl Vect and Mat Operations

1.2.3. Multiplication

COMCOLCST (Code 34352, NOV/81)
COMROWCST (Code 34353, NOV/81)

1.2.4. Scalar Products

COMMATVEC (Code 34354, NOV/81)
HSHCOMCOL (Code 34355, NOV/81)
HSHCOMPRD (Code 34356, NOV/81)

1.2.5. Elimination

ELMCOMVECCOL (Code 34376, NOV/81)
ELMCOMCOL (Code 34377, NOV/81)
ELMCOMROWVEC (Code 34378, NOV/81)

1.2.6. Interchanging

1.2.7. Rotation

ROTCOMCOL (Code 34357, NOV/81)
ROTCOMROW (Code 34358, NOV/81)
CHSH2 (Code 34611, NOV/81)

1.2.8. Norms

COMEUCNRM (Code 34359, NOV/81)

1.2.9. Scaling

COMSCL (Code 34193, NOV/81)
SCLCOM (Code 34360, NOV/81)

1.3. Complex Arithmetic

1.3.1. Monadic Operations

COMABS (Code 34340, NOV/81)
COMSQRT (Code 34343, NOV/81)
CARPOL (Code 34344, NOV/81)

1.3.2. Dyadic Operations

COMMUL (Code 34341, NOV/81)
COMDIV (Code 34342, NOV/81)

1.4. Long Integer Arithmetic

LNGINTADD (Code 31200, NOV/81)
LNGINTSUBTRACT (Code 31201, NOV/81)
LNGINTMULT (Code 31202, NOV/81)
LNGINTDIVIDE (Code 31203, NOV/81)
LNGINTPOWER (Code 31204, NOV/81)

1.5. Long Real Arithmetic

1.5.1. Elem. Arithmetic Operations

DP ADD (Code 31101, NOV/81)
DP SUB (Code 31102, NOV/81)
DP MUL (Code 31103, NOV/81)
DP DIV (Code 31104, NOV/81)
DP POW (Code 31109, NOV/81)
LNG ADD (Code 31105, NOV/81)
LNG SUB (Code 31106, NOV/81)
LNG MUL (Code 31107, NOV/81)
LNG DIV (Code 31108, NOV/81)
LNG POW (Code 31110, NOV/81)

1.5.2. Scalar Products

LNGVECVEC (Code 34410, NOV/81)
LNGMATVEC (Code 34411, NOV/81)
LNGTAMVEC (Code 34412, NOV/81)
LNGMATMAT (Code 34413, NOV/81)
LNGTAMMAT (Code 34414, NOV/81)
LNGMATTAM (Code 34415, NOV/81)
LNGSEQVEC (Code 34416, NOV/81)
LNGSCAPRD1 (Code 34417, NOV/81)
LNGSYMMATVEC (Code 34418, NOV/81)
LNGFULMATVEC (Code 31505, NOV/81)
LNGFULTAMVEC (Code 31506, NOV/81)
LNGFULSYMMATVEC (Code 31507, NOV/81)
LNGRESVEC (Code 31508, NOV/81)
LNGSYMRESVEC (Code 31509, NOV/81)

1.5.3. Conversion

LNGREATODECI (Code 31100, NOV/81)

2. Algebraic Evaluations

2.1. Eval. of a Finite Series

2.2. Eval. of Polynomials

2.2.1. Eval. of General Polynomials

2.2.1.1. Polynomials in Grunert Form

POL (Code 31040, NOV/81)
TAYPOL (Code 31241, NOV/81)
NORDERPOL (Code 31242, NOV/81)
DERPOL (Code 31243, NOV/81)

2.2.1.2. Polynomials in Newton Form

2.2.2. Eval. of Orthogon. Polynomials

2.2.2.1. General Orthogon. Polynomials

ORTPOL (Code 31044, NOV/81)
ORTPOLSYM (Code 31048, NOV/81)
ALLORTPOL (Code 31045, NOV/81)
ALLORTPOLSYM (Code 31049, NOV/81)
SUMORTPOL (Code 31047, NOV/81)
SUMORTPOLSYM (Code 31058, NOV/81)

2.2.2.2. Chebychev Polynomials

CHEPOLSUM (Code 31046, NOV/81)
ODDCHEPOLSUM (Code 31059, NOV/81)
CHEPOL (Code 31042, NOV/81)
ALLCHEPOL (Code 31043, NOV/81)

2.2.3. Eval. of Trigonom. Polynomials

2.2.3.1. Eval. of Fourier Series

SINSER (Code 31090, NOV/81)
COSSER (Code 31091, NOV/81)
FOUSER (Code 31092, NOV/81)
FOUSER1 (Code 31093, NOV/81)
FOUSER2 (Code 31094, NOV/81)
COMFOUSER (Code 31095, NOV/81)
COMFOUSER1 (Code 31096, NOV/81)
COMFOUSER2 (Code 31097, NOV/81)

2.3. Eval. of Continued Fractions

JFRAC (Code 35083, NOV/81)

2.4. Operations On Polynomials

2.4.1. Transf. of Representation

POLCHS (Code 31051, NOV/81)
CHSPOL (Code 31052, NOV/81)
POLSHTCHS (Code 31053, NOV/81)
SHTCHSPOL (Code 31054, NOV/81)
GRNNEW (Code 31055, NOV/81)
NEWGRN (Code 31050, NOV/81)
LINTFMPOL (Code 31250, NOV/81)

2.4.2. Op. On General Polynomials

2.4.3. Op. On Orthogonal Polynomials

INTCHS (Code 31248, NOV/81)

2.5. Fast Fourier Transform

3. Linear Algebra

3.1. Linear Systems

3.1.1. Full Matrices

3.1.1.1. Square Non-singular Matrices

3.1.1.1.1. Real Matrices

3.1.1.1.1.1. General Matrices

3.1.1.1.1.1.1. Preparatory Procedures

DEC (Code 34300, NOV/81)
GSSELM (Code 34231, NOV/81)
ONENRMINV (Code 34240, NOV/81)
ERBELM (Code 34241, NOV/81)
GSSERB (Code 34242, NOV/81)
GSSNRI (Code 34252, NOV/81)

3.1.1.1.1.1.2. Calculation of Determinant

DETERM (Code 34303, NOV/81)

3.1.1.1.1.1.3. Solution of Linear Equations

SOL (Code 34051, NOV/81)
DECSOL (Code 34301, NOV/81)
SOLELM (Code 34061, NOV/81)
GSSSOL (Code 34232, NOV/81)
GSSSOLERB (Code 34243, NOV/81)

3.1.1.1.1.1.4. Matrix Inversion

INV (Code 34053, NOV/81)
DECINV (Code 34302, NOV/81)
INV1 (Code 34235, NOV/81)
GSSINV (Code 34236, NOV/81)
GSSINVERB (Code 34244, NOV/81)

3.1.1.1.1.1.5. Iteratively Improved Solution

ITISOL (Code 34250, NOV/81)
GSSITISOL (Code 34251, NOV/81)
ITISOLERB (Code 34253, NOV/81)
GSSITISOLERB (Code 34254, NOV/81)

3.1.1.1.1.2. Symmetric Pos Def Matrices

3.1.1.1.1.2.1. Preparatory Procedures

CHLDEC2 (Code 34310, NOV/81)
CHLDEC1 (Code 34311, NOV/81)

3.1.1.1.1.2.2. Calculation of Determinant

CHLDETERM2 (Code 34312, NOV/81)
CHLDETERM1 (Code 34313, NOV/81)

3.1.1.1.1.2.3. Solution of Linear Equations

CHLSOL2 (Code 34390, NOV/81)
CHLSOL1 (Code 34391, NOV/81)
CHLDECSOL2 (Code 34392, NOV/81)
CHLDECSOL1 (Code 34393, NOV/81)

3.1.1.1.1.2.4. Matrix Inversion

CHLINV2 (Code 34400, NOV/81)
CHLINV1 (Code 34401, NOV/81)
CHLDECINV2 (Code 34402, NOV/81)
CHLDECINV1 (Code 34403, NOV/81)

3.1.1.1.1.3. General Symmetric Matrices

3.1.1.1.1.3.1. Preparatory Procedures

DECSYM2 (Code 34291, NOV/81)

3.1.1.1.1.3.2. Calculation of Determinant

DETERMSYM2 (Code 34294, NOV/81)

3.1.1.1.1.3.3. Solution of Linear Equations

SOLSYM2 (Code 34292, NOV/81)
DECSOLSYM2 (Code 34293, NOV/81)

3.1.1.1.2. Complex Matrices

3.1.1.2. Full Rank Overdeterm Systems

3.1.1.2.1. Real Matrices

3.1.1.2.1.1. Preparatory Procedures

LSQORTDEC (Code 34134, NOV/81)
LSQDGLINV (Code 34132, NOV/81)

3.1.1.2.1.2. Least Squares Solution

LSQSOL (Code 34131, NOV/81)
LSQORTDECSOL (Code 34135, NOV/81)

3.1.1.2.1.3. Inverse Matrix of Normal Eqn.

LSQINV (Code 34136, NOV/81)

3.1.1.2.1.4. Least Sqrs with Lin. Constr.

LSQDECOMP (Code 34137, NOV/81)
LSQREFSOL (Code 34138, NOV/81)

3.1.1.2.2. Complex Matrices

3.1.1.3. Other Problems

3.1.1.3.1. Real Matrices

3.1.1.3.1.1. Solution Overdetermined Syst

SOLSVDOVR (Code 34280, NOV/81)
SOLOVR (Code 34281, NOV/81)

3.1.1.3.1.2. Solution Underdeterm Systems

SOLSVDUND (Code 34282, NOV/81)
SOLUND (Code 34283, NOV/81)

3.1.1.3.1.3. Solution Homogeneous Equation

HOMSOLSVD (Code 34284, NOV/81)
HOMSOL (Code 34285, NOV/81)

3.1.1.3.1.4. Pseudo-inversion

PSDINVSVD (Code 34286, NOV/81)
PSDINV (Code 34287, NOV/81)

3.1.1.3.2. Complex Matrices

3.1.2. Sparse Matrices

3.1.2.1. Direct Methods

3.1.2.1.1. Real Matrices

3.1.2.1.1.1. Non-symmetric Matrices

3.1.2.1.1.1.1. Band Matrices

3.1.2.1.1.1.1.1. Preparatory Procedures

DECBND (Code 34320, NOV/81)

3.1.2.1.1.1.1.2. Calculation of Determinant

DETERMBND (Code 34321, NOV/81)

3.1.2.1.1.1.1.3. Solution of Linear Equations

SOLBND (Code 34071, NOV/81)
DECSOLBND (Code 34322, NOV/81)

3.1.2.1.1.1.2. Tridiagonal Matrices

3.1.2.1.1.1.2.1. Preparatory Procedures

DECTRI (Code 34423, NOV/81)
DECTRIPIV (Code 34426, NOV/81)

3.1.2.1.1.1.2.2. Calculation of Determinant

3.1.2.1.1.1.2.3. Solution of Linear Equations

SOLTRI (Code 34424, NOV/81)
DECSOLTRI (Code 34425, NOV/81)
SOLTRIPIV (Code 34427, NOV/81)
DECSOLTRIPIV (Code 34428, NOV/81)

3.1.2.1.1.1.3. Bloc-tridiagonal Matrices

3.1.2.1.1.2. Symmetric Pos Def Matrices

3.1.2.1.1.2.1. Band Matrices

3.1.2.1.1.2.1.1. Preparatory Procedures

CHLDECBND (Code 34330, NOV/81)

3.1.2.1.1.2.1.2. Calculation of Determinant

CHLDETERMBND (Code 34331, NOV/81)

3.1.2.1.1.2.1.3. Solution of Linear Equations

CHLSOLBND (Code 34332, NOV/81)
CHLDECSOLBND (Code 34333, NOV/81)

3.1.2.1.1.2.2. Tridiagonal Matrices

3.1.2.1.1.2.2.1. Preparatory Procedures

DECSYMTRI (Code 34420, NOV/81)

3.1.2.1.1.2.2.2. Calculation of Determinant

3.1.2.1.1.2.2.3. Solution of Linear Equations

SOLSYMTRI (Code 34421, NOV/81)
DECSOLSYMTRI (Code 34422, NOV/81)

3.1.2.1.1.2.3. Bloc-tridiagonal Matrices

3.1.2.1.2. Complex Matrices

3.1.2.2. Iterative Methods

3.1.2.2.1. Real Matrices

CONJ GRAD (Code 34220, NOV/81)

3.1.2.2.2. Complex Matrices

3.2. Transformation to Special Form

3.2.1. Similarity Transformations

3.2.1.1. Equilibration

3.2.1.1.1. Real Matrices

EQILBR (Code 34173, NOV/81)
BAKLBR (Code 34174, NOV/81)

3.2.1.1.2. Complex Matrices

EQILBRCOM (Code 34361, NOV/81)
BAKLBRCOM (Code 34362, NOV/81)

3.2.1.2. Transf to Hessenberg Form

3.2.1.2.1. Real Matrices

3.2.1.2.1.1. Symmetric Matrices

TFMSYMTRI2 (Code 34140, NOV/81)
BAKSYMTRI2 (Code 34141, NOV/81)
TFMPREVEC (Code 34142, NOV/81)
TFMSYMTRI1 (Code 34143, NOV/81)
BAKSYMTRI1 (Code 34144, NOV/81)

3.2.1.2.1.2. Asymmetric Matrices

TFMREAHES (Code 34170, NOV/81)
BAKREAHES1 (Code 34171, NOV/81)
BAKREAHES2 (Code 34172, NOV/81)

3.2.1.2.2. Complex Matrices

3.2.1.2.2.1. Hermitian Matrices

HSHHRMTRI (Code 34363, NOV/81)
HSHHRMTRIVAL (Code 34364, NOV/81)
BAKHRMTRI (Code 34365, NOV/81)

3.2.1.2.2.2. Non-hermitian Matrices

HSHCOMHES (Code 34366, NOV/81)
BAKCOMHES (Code 34367, NOV/81)

3.2.2. Other Transformations

3.2.2.1. Transf to Bidiagonal Form

3.2.2.1.1. Real Matrices

HSHREABID (Code 34260, NOV/81)
PSTTFMMAT (Code 34261, NOV/81)
PRETFMMAT (Code 34262, NOV/81)

3.2.2.1.2. Complex Matrices

3.3. The (ordinary) Eigenv Problem

3.3.1. Real Matrices

3.3.1.1. Symmetric Matrices

3.3.1.1.1. Tridiagonal Matrices

VALSYMTRI (Code 34151, NOV/81)
VECSYMTRI (Code 34152, NOV/81)
QRIVALSYMTRI (Code 34160, NOV/81)
QRISYMTRI (Code 34161, NOV/81)

3.3.1.1.2. Full Matrices

EIGVALSYM2 (Code 34153, NOV/81)
EIGSYM2 (Code 34154, NOV/81)
EIGVALSYM1 (Code 34155, NOV/81)
EIGSYM1 (Code 34156, NOV/81)
QRIVALSYM2 (Code 34162, NOV/81)
QRISYM (Code 34163, NOV/81)
QRIVALSYM1 (Code 34164, NOV/81)

3.3.1.1.3. Iterative Improvement

3.3.1.1.3.1. Auxiliary Procedures

MERGESORT (Code 36405, NOV/81)
VECPERM (Code 36404, NOV/81)
ROWPERM (Code 36403, NOV/81)

3.3.1.1.3.2. Orthogonalisation

ORTHOG (Code 36402, NOV/81)

3.3.1.1.3.3. Improvement and Errorbounds

SYMEIGINP (Code 36401, NOV/81)

3.3.1.2. Asymmetric Matrices

3.3.1.2.1. Matrices in Hessenberg Form

REAVALQRI (Code 34180, NOV/81)
REAVECHES (Code 34181, NOV/81)
REAQRI (Code 34186, NOV/81)
COMVALQRI (Code 34190, NOV/81)
COMVECHES (Code 34191, NOV/81)

3.3.1.2.2. Full Matrices

REAEIGVAL (Code 34182, NOV/81)
REAEIG1 (Code 34184, NOV/81)
REAEIG3 (Code 34187, NOV/81)
COMEIGVAL (Code 34192, NOV/81)
COMEIG1 (Code 34194, NOV/81)

3.3.2. Complex Matrices

3.3.2.1. Hermitian Matrices

EIGVALHRM (Code 34368, NOV/81)
EIGHRM (Code 34369, NOV/81)
QRIVALHRM (Code 34370, NOV/81)
QRIHRM (Code 34371, NOV/81)

3.3.2.2. Non-hermitian Matrices

3.3.2.2.1. Matrices in Hessenberg Form

VALQRICOM (Code 34372, NOV/81)
QRICOM (Code 34373, NOV/81)

3.3.2.2.2. Full Matrices

EIGVALCOM (Code 34374, NOV/81)
EIGCOM (Code 34375, NOV/81)

3.4. The Generalized Eigenv Problem

3.4.1. Real Matrices

3.4.1.1. Symmetric Matrices

3.4.1.2. Asymmetric Matrices

QZIVAL (Code 34600, NOV/81)
QZI (Code 34601, NOV/81)
HSHDECMUL (Code 34602, NOV/81)
HESTGL3 (Code 34603, NOV/81)
HESTGL2 (Code 34604, NOV/81)
HSH2COL (Code 34605, NOV/81)
HSH3COL (Code 34606, NOV/81)
HSH2ROW3 (Code 34607, NOV/81)
HSH2ROW2 (Code 34608, NOV/81)
HSH3ROW3 (Code 34609, NOV/81)
HSH3ROW2 (Code 34610, NOV/81)

3.5. Singular Values

3.5.1. Real Matrices

3.5.1.1. Bidiagonal Matrices

QRISNGVALBID (Code 34270, NOV/81)
QRISNGVALDECBID (Code 34271, NOV/81)

3.5.1.2. Full Matrices

QRISNGVAL (Code 34272, NOV/81)
QRISNGVALDEC (Code 34273, NOV/81)

3.5.2. Complex Matrices

3.6. Zeros of Polynomials

3.6.1. Zeros of General Real Polynom.

ZERPOL (Code 34501, NOV/81)
BOUNDS (Code 34502, NOV/81)

3.6.2. Zeros of Orthogonal Polynom.

ALLZERORTPOL (Code 31362, NOV/81)
LUPZERORTPOL (Code 31363, NOV/81)
SELZERORTPOL (Code 31364, NOV/81)
ALLJACZER (Code 31370, NOV/81)
ALLLAGZER (Code 31371, NOV/81)

3.6.3. Zeros of Complex Polynomials

COMKWD (Code 34345, NOV/81)

4. Analytic Evaluations

4.1. Eval. of An Infinite Series

EULER (Code 32010, NOV/81)
SUMPOSSERIES (Code 32020, NOV/81)

4.2. Quadrature

4.2.1. One-dimensional Quadrature

QADRAT (Code 32070, NOV/81)
INTEGRAL (Code 32051, NOV/81)

4.2.2. Multidimensional Quadrature

TRICUB (Code 32075, NOV/81)

4.2.3. Gaussian Quadrature

4.2.3.1. General Weights

RECCOF (Code 31254, NOV/81)
GSSWTS (Code 31253, NOV/81)
GSSWTSSYM (Code 31252, NOV/81)

4.2.3.2. Special Weights

GSSJACWGHTS (Code 31425, NOV/81)
GSSLAGWGHTS (Code 31427, NOV/81)

4.3. Numerical Differentiation

4.3.1. Functions of One Variable

4.3.2. Functions of More Variables

4.3.2.1. Calc. with Difference Formulas

JACOBNNF (Code 34437, NOV/81)
JACOBNMF (Code 34438, NOV/81)
JACOBNBNDF (Code 34439, NOV/81)

5. Analytical Problems

5.1. Analytical Equations

5.1.1. Non-linear Equations

5.1.1.1. A Single Equation

5.1.1.1.1. No Derivative Available

ZEROIN (Code 34150, NOV/81)
ZEROINRAT (Code 34436, NOV/81)

5.1.1.1.2. Derivative Available

ZEROINDER (Code 34453, NOV/81)

5.1.1.2. A System of Equations

5.1.1.2.1. Auxiliary Procedures

5.1.1.2.2. Jacobian Matrix Not Available

QUANEWBND (Code 34430, NOV/81)
QUANEWBND1 (Code 34431, NOV/81)

5.1.1.2.3. Jacobian Matrix Available

5.1.1.3. Polynomial Equations ( See Also Section 3.6 )

5.1.2. Unconstrained Optimization

5.1.2.1. Functions of One Variable

5.1.2.1.1. Derivative Not Available

MININ (Code 34433, NOV/81)

5.1.2.1.2. Derivative Available

MININDER (Code 34435, NOV/81)

5.1.2.2. Functions of More Variables

5.1.2.2.1. Auxiliary Procedures

LINEMIN (Code 34210, NOV/81)
RNK1UPD (Code 34211, NOV/81)
DAVUPD (Code 34212, NOV/81)
FLEUPD (Code 34213, NOV/81)

5.1.2.2.2. No Derivatives Available

PRAXIS (Code 34432, NOV/81)

5.1.2.2.3. Gradient Available

RNK1MIN (Code 34214, NOV/81)
FLEMIN (Code 34215, NOV/81)

5.1.2.2.4. Gradient & Jacobian Available

5.1.3. Overdetermined Nonlinear Syst.

5.1.3.1. Least Squares Solutions ( See Also Section 7. )

5.1.3.1.1. Auxiliary Procedures

5.1.3.1.2. Jacobian Matrix Not Available (see Also Section 5.1.2.2.2. )

5.1.3.1.3. Jacobian Matrix Available

MARQUARDT (Code 34440, NOV/81)
GSSNEWTON (Code 34441, NOV/81)

5.2. Functional Equations

5.2.1. Differential Equations

5.2.1.1. Initial Value Problems

5.2.1.1.1. First Order Ordinary D.e.

5.2.1.1.1.1. No Derivatives Rhs Available

RK1 (Code 33010, NOV/81)
RKE (Code 33033, NOV/81)
RK4A (Code 33016, NOV/81)
RK4NA (Code 33017, NOV/81)
RK5NA (Code 33018, NOV/81)
MULTISTEP (Code 33080, NOV/81)
DIFFSYS (Code 33180, NOV/81)
ARK (Code 33061, NOV/81)
EFRK (Code 33070, NOV/81)

5.2.1.1.1.2. Jacobian Matrix Available ( See Also Proc. Multistep 5.2.1.1.1.1 )

EFSIRK (Code 33160, NOV/81)
EFERK (Code 33120, NOV/81)
LINIGER1VS (Code 33132, NOV/81)
LINIGER2 (Code 33131, NOV/81)
GMS (Code 33191, NOV/81)
IMPEX (Code 33135, NOV/81)

5.2.1.1.1.3. Several Derivatives Available

MODIFIED TAYLOR (Code 33040, NOV/81)
EXPONENTIALLY FITTED TAYLOR (Code 33050, NOV/81)

5.2.1.1.2. Second Order Ordinary D.e.

5.2.1.1.2.1. No Derivatives Rhs Available

RK2 (Code 33012, NOV/81)
RK2N (Code 33013, NOV/81)
RK3 (Code 33014, NOV/81)
RK3N (Code 33015, NOV/81)

5.2.1.1.2.2. Several Deriv. Rhs Available

5.2.1.1.3. Initial Boundary Value Problem

ARKMAT (Code 33066, NOV/81)

5.2.1.2. Boundary Value Problems

5.2.1.2.1. Two Point B.v.p.

5.2.1.2.1.1. Shooting Methods ( See Also Section 5.2.1.3.1 )

5.2.1.2.1.2. Linear Global Methods

5.2.1.2.1.2.1. Second Order Tpbvp

5.2.1.2.1.2.1.1. Self Adjoint Tpbvp

FEM LAG SYM (Code 33300, NOV/81)
FEM LAG (Code 33301, NOV/81)
FEM LAG SPHER (Code 33308, NOV/81)

5.2.1.2.1.2.1.2. Skew Adjoint Tpbvp

FEM LAG SKEW (Code 33302, NOV/81)

5.2.1.2.1.2.2. Fourth Order Tpbvp

5.2.1.2.1.2.2.1. Self Adjoint Tpbvp

FEM HERM SYM (Code 33303, NOV/81)

5.2.1.2.1.2.2.2. Skew Adjoint Tpbvp

5.2.1.2.1.3. Non-linear Global Methods

NON LIN FEM LAG SKEW (Code 33314, NOV/81)

5.2.1.2.2. Two-dimensional B.v.p.

5.2.1.2.2.1. Elliptic B.v.p.s

5.2.1.2.2.1.1. Discretization Procedures

5.2.1.2.2.1.2. Special Linear Systems ( See Also Section 3.1.2 )

RICHARDSON (Code 33170, NOV/81)
ELIMINATION (Code 33171, NOV/81)

5.2.1.2.2.1.3. Special Non-linear Systems

5.2.1.2.2.2. Parabolic & Hyperbolic B.v.p.s

5.2.1.2.3. Multi-dimensional B.v.p.

5.2.1.2.4. Over-determined Problems

5.2.1.3. Parameter Estimation in D.e.

5.2.1.3.1. P.e. in Initial Value Problems

PEIDE (Code 34444, NOV/81)

5.2.2. Integral Equations

5.2.3. Integro- Differential Eqs

5.2.4. Difference Equations

5.2.5. Convolution Equations

6. Special Functions & Constants

6.1. Mathematical Constants

PI (Code 30006, NOV/81)
E (Code 30007, NOV/81)

6.2. Machine Constants

MBASE (Code 30001, NOV/81)
ARREB (Code 30002, NOV/81)
DWARF (Code 30003, NOV/81)
GIANT (Code 30004, NOV/81)
INTCAP (Code 30005, NOV/81)
OVERFLOW (Code 30008, NOV/81)
UNDERFLOW (Code 30009, NOV/81)

6.3. Random Numbers

6.4. Elementary Functions

6.4.1. Circular Functions

TAN (Code 35120, NOV/81)
ARCSIN (Code 35121, NOV/81)
ARCCOS (Code 35122, NOV/81)

6.4.2. Hyperbolic Functions

SINH (Code 35111, NOV/81)
COSH (Code 35112, NOV/81)
TANH (Code 35113, NOV/81)
ARCSINH (Code 35114, NOV/81)
ARCCOSH (Code 35115, NOV/81)
ARCTANH (Code 35116, NOV/81)

6.4.3. Logarithmic Function

LOG ONE PLUS X (Code 35130, NOV/81)

6.5. Exponential Integral, Etc.

6.5.1. Exponential Integral

EI (Code 35080, NOV/81)
EI ALPHA (Code 35081, NOV/81)
ENX (Code 35086, NOV/81)
NONEXP ENX (Code 35087, NOV/81)

6.5.2. Sine and Cosine Integral

SINCOSINT (Code 35084, NOV/81)
SINCOSFG (Code 35085, NOV/81)

6.6. Gamma Function, Etc.

GAMMA (Code 35061, NOV/81)
RECIP GAMMA (Code 35060, NOV/81)
LOG GAMMA (Code 35062, NOV/81)
INCOMGAM (Code 35030, NOV/81)
INCBETA (Code 35050, NOV/81)
IBPPLUSN (Code 35051, NOV/81)
IBQPLUSN (Code 35052, NOV/81)
IXQFIX (Code 35053, NOV/81)
IXPFIX (Code 35054, NOV/81)
FORWARD (Code 35055, NOV/81)
BACKWARD (Code 35056, NOV/81)

6.7. Error Function, Etc.

ERRORFUNCTION (Code 35021, NOV/81)
NONEXPERFC (Code 35022, NOV/81)
INVERSE ERROR FUNCTION (Code 35023, NOV/81)
FRESNEL (Code 35027, NOV/81)
FG (Code 35028, NOV/81)

6.8. Legendre Functions

6.9. Bessel Functions of Int. Order

6.9.1. Bessel Functions J and Y

BESS J0 (Code 35160, NOV/81)
BESS J1 (Code 35161, NOV/81)
BESS J (Code 35162, NOV/81)
BESS Y01 (Code 35163, NOV/81)
BESS Y (Code 35164, NOV/81)
BESS PQ0 (Code 35165, NOV/81)
BESS PQ1 (Code 35166, NOV/81)