UC San Diego technical report, August 2010.
Official technical manual: IEEE Arithmetic.
Relevant locators: IEEE Arithmetic Model, significand precision and overall bit count; Double Format, field layout and Table 2-5; and Ranges and Precisions in Decimal Representation. The source describes the traditional IEEE double format, now called binary64. It supports the precision and storage calculations for the double-precision floating-point format; no claim about a current processor's execution speed is inferred.
The “Caveats” subsection derives the loss of position accuracy proportional to the square root of function-value relative accuracy near a nonzero minimum with positive second derivative. “Minimization Algorithms” describes golden-section search and its linear contraction. The claims concern standard mathematical precision effects, not an assertion that later software releases were available for a historical examination.
The NEOS Guide's mathematical account of quasi-Newton methods, deriving the secant condition from an integrated Hessian matrix and describing low-rank updating, including BFGS. The related nonlinear-equation account is neos-guide.org/guide/algorithms/broyden/ and discusses Broyden's method.
Cited passages: William L. Briggs, A Multigrid Tutorial, presented by Van Emden Henson, slides 59–63: correction and recursive V-cycle.
Foundations and Trends in Optimization 1(4), 241–433; DOI 10.1561/2400000006. PDF lists the volume issue year as 2014 and copyright as 2015; author-hosted course reference and institutional publication record identify 2015.
Cited passages: §4.1–4.2, Algorithm 4.2; §9.1, equation 9.2 and Theorem 9.1.
Cited passages: James Demmel, CS267 supplemental notes, 12 March 1996, How Multigrid Damps High Frequencies: sine eigenvectors and the one-third high-frequency bound.
Additional cited passages: diagonal-2 tridiagonal Poisson matrix, error eigenvector expansion, weighted-iteration multiplier, and concluding attenuation statement. The heading dates the lecture to 12 March 1996.
Cited passages: Long Chen, Introduction to Multigrid Methods, 17 December 2011, section 2: plain Jacobi retains both extreme sine modes; Long Chen, Introduction to Multigrid Methods, 17 December 2011, sections 4–5: energy projection, transfer matrices, and Galerkin triple product; the displayed cancellation identities follow by direct substitution.
Cited passages: Achi Brandt, Multi-Level Adaptive Solutions to Boundary-Value Problems, Mathematics of Computation 31(138), April 1977, pp. 333–390, abstract and introduction.
Cited passages: Christian Clason, Introduction to Finite Element Methods, §2.2, Theorem 2.7(ii): continuity bound; Clason, Introduction to Finite Element Methods, §2.2, Theorem 2.7, pp. 20–21, equation (2.9): hypotheses, unique solvability and load bound.
Cited passages: Tobin A. Driscoll and Richard J. Braun, Fundamentals of Numerical Computation, §5.6.1, equations 5.6.3–5.6.5: integrating the piecewise linear interpolant.
Online text: fncbook.com/lu/
Additional cited passages: §2.8, Definition 2.8.1 and equation (2.8.5); §2.8.1, Theorem 2.8.1 and equation (2.8.6), right-hand-side perturbation bound. The online edition is undated; Tobin A. Driscoll and Richard J. Braun are the whole-book coauthors, with no separate section byline.
Online text: fncbook.com/rk/
Cited passages: Fundamentals of Numerical Computation, §6.4.3, equations 6.4.10–6.4.11: multistage recipe and tableau.
§5.7 of the authors’ online textbook. Its difference-based error estimation is distinguished from a universal accuracy guarantee; no online-edition date is inferred.
Cited passages: §5.7.1, equation 5.7.4: a difference-based error estimate; §5.7.2: interval bisection; Example 5.7.2 and concluding discussion: requested accuracy is not guaranteed.
Collection of sources; individual chapter authors and dates are recorded below.
Publisher: SIAM.
Cited passages: Hermitian Eigenvalue Problems → Single- and Multiple-Vector Iterations → Power Method, introductory paragraph: largest absolute eigenvalue and corresponding eigenvector; Hermitian Eigenvalue Problems → Single- and Multiple-Vector Iterations → Power Method, paragraph after the angle definition: perpendicular starting vector fails to select the dominant eigenvector in exact arithmetic.
Cited passages: Non-Hermitian Eigenvalue Problems → Single- and Multiple-Vector Iterations → Power Method, convergence paragraph: largest magnitude eigenvalue and spectral-ratio rate.
Collection of sources; individual chapter authors and dates are recorded below.
Cited passages: Changing shifts, §3, PDF p. 3: approximate eigenvector equation and Rayleigh quotient; Power iteration, §1, PDF pp. 1–2: diagonalizable expansion and nonzero first coordinate of the starting vector.
Publisher: Netlib.
Cited passages: LAPACK DGETRS, A argument: factors from DGETRF satisfy ; LAPACK DGETRS, version 3.3.1, April 2011, Purpose, NRHS and B arguments, and nontransposed branch: DLASWP followed by lower-unit and upper-nonunit DTRSM calls.
Publisher: SIAM.
Cited passages: Rarefaction wave, full piecewise solution; expansion-shock example; The entropy condition; Shock solution; Rarefaction wave; The entropy condition.
Publisher: Cambridge University Press.
Cited passages: Appendix A.5.2, pp. 646–647: symmetric eigenvalue decomposition and definiteness; §2.2.2, p. 30, equation (2.3): ellipsoids and semi-axis lengths; the book uses the inverse quadratic coefficient matrix; §3.1.4, Example 3.2, p. 71: a quadratic function is strictly convex exactly when its symmetric coefficient matrix is positive definite.
Cited passages: Appendix A.5.5, printed p. 650: block inversion and minimized quadratic form; §C.4.1, printed pp. 672–675: block elimination, Algorithm C.4, factor-solve interpretation and dense complexity.
The front matter states first publication in 2004 and a seventh printing with corrections in 2009. The title page credits Stephen Boyd and Lieven Vandenberghe as whole-book coauthors; no separate appendix byline is supplied. Cambridge University Press publishes the book; the Stanford author website hosts this copy.
Cited passages: Appendix A.1.6, printed pp. 636–637, dual norms.
Additional cited passage: §2.1.4, printed p. 24 (PDF page index 37), convex combinations and the definition and minimality of the convex hull. The title-page whole-book credits and the separately recorded 2004 first publication and 2009 corrected seventh printing apply to this copy.
Additional cited passages: §5.6.3, printed pp. 251–253, especially equation (5.58), local sensitivity of the optimal value to equality-constraint perturbations. The sign of the Lagrange multiplier depends on the chosen sign for the equality term. The title page and front matter retain the whole-book authorship, 2004 first publication and 2009 corrected seventh printing recorded above.
Additional locators: §§5.1–5.2, pp.215–227.
Additional cited passage: §4.4.2, printed p. 157, equation (4.37), robust linear programming imposes each inequality for every parameter in the chosen uncertainty set. The illustrated set is an ellipsoid, and its worst-case linear contribution is a Euclidean norm; a box or finite sign model has a different support calculation. [ref]
Publisher: SciPy project.
The scipy.stats.multivariate_normal Notes describe singular covariance using a pseudo-determinant, pseudoinverse and covariance rank when singular evaluation is allowed. The pinned implementation separately checks the covariance support: _PSD._support_mask tests the null-space residual against its numerical tolerance, and multivariate_normal_gen.pdf/logpdf return zero density or negative-infinite log density off support. [ref] [ref]
Covariance.whiten describes transforming observations to whitened coordinates. Its example constructs Covariance.from_precision from a positive-definite covariance, whitens a Gaussian sample and displays a near-identity sample covariance. [ref]
The scipy.stats.norm method list identifies cdf as the cumulative distribution function, sf as the survival function, and ppf as the inverse cdf. The loc and scale parameters specify the mean and standard deviation. The documentation notes that sf can be more accurate than subtracting cdf from one when evaluating a tail. [ref]
The scipy.stats.uniform description specifies the standard uniform distribution on the unit interval and the loc/scale transformation to the interval from loc to loc plus scale. Its Methods list includes rvs for random variates, alongside cdf and ppf. [ref]
The scipy.signal.group_delay definition differentiates continuous unwrapped phase with respect to digital angular frequency and reports delay in samples; the fs parameter sets the frequency units. An analog derivative with respect to angular frequency in radians per second instead yields seconds. [ref]
Notes: standardized folded-normal density, nonnegative shape parameter and loc/scale transformation. Taking the absolute value of a normal variable with mean and standard deviation corresponds to shape , loc=0 and scale=s.
The scipy.stats.multivariate_normal cdf method evaluates joint lower-orthant probabilities using the specified mean vector and covariance matrix. Its maxpts, abseps, and releps arguments control numerical integration limits and tolerances; lower_limit specifies the lower integration bounds. This supports evaluating a correlated maximum at a vector of equal upper thresholds without multiplying marginal probabilities. [ref]
The scipy.fft.fft norm parameter documents an unscaled forward transform for the default backward convention, a 1/n-scaled forward transform for forward, and symmetric 1/sqrt(n) scaling for ortho. Its Notes specify the negative-exponent forward sum, ordering of positive and negative frequencies, and conjugate symmetry for real inputs. [ref]
The scipy.stats.binom Notes define the binomial mass function, including its positive probability at zero for a finite nondegenerate calibration sample; pmf evaluates each count probability. [ref]
The signal-processing guide Spectral Analysis section derives the sinc leakage of a finite-duration sinusoid and discusses the tradeoff between window main-lobe width and sidelobe height. [ref]
The scipy.signal.periodogram scaling parameter distinguishes squared spectrum units from power spectral density units. Its Notes give the window-dependent spectrum/density conversion and one-sided power folding; its flattop example estimates RMS amplitude from the square root of a spectrum peak. [ref]
BinomTestResult.proportion_ci documents its confidence_level parameter, the exact binomial proportion-interval method, and the low/high attributes of the returned bounds. These are parameter-estimation bounds; scipy.stats.binom.interval instead describes count-distribution intervals for supplied parameters. [ref] [ref]
scipy.signal.windows.boxcar, description and Returns: the rectangular window uses all-ones coefficients. scipy.signal.windows.hann, sym parameter, Returns and Notes: the symmetric endpoint convention differs from the periodic spectral convention; the documented even-length symmetric array need not attain coefficient one.
scipy.ndimage.zoom, description and order parameter: array zoom uses spline interpolation of the requested order, with orders zero through five; resizing is a numerical reconstruction operation rather than an additional physical measurement.
scipy.signal.freqz, defining frequency-response sum; Parameters: fs; Returns: w: evaluates a finite numerator/denominator frequency response; the default frequency unit is radians per sample, with frequencies expressed in the same units as fs when supplied.
null_space, lines 333–403: the pinned function constructs a null-space basis from right singular vectors after SVD; rcond controls the relative cutoff for effective numerical rank. The returned basis Q uses vh[num:,:].T.conj().
scipy.stats.chi2, Notes: the chi-squared density and its gamma-distribution representation supply the density used in the explicitly derived reciprocal-moment calculation.
Cited passages: solve_ivp, method parameter: explicit versus implicit methods and stiffness; solve_ivp, rtol and atol parameters: local error estimates, additive scaling and component-specific atol.
Publisher: LAPACK project (Netlib hosting).
Cited passages: DLARTG, LAPACK 3.12.1, Purpose: block, signed R, scaling and zero-input cases; implementation lines 137–159.
Publisher: LAPACK project (Netlib hosting).
This source is credited to an organization.
Cited passages: DROT source, lines 116–120 and 130–134: temporary first-row value and second-row update.
Published in Mathematical Programming, Series B, 69(1), 205–236.
Cited passages: Publication record and authored abstract: A Primal-Dual Potential Reduction Method for Problems Involving Matrix Inequalities, Mathematical Programming, Series B, 69(1), 205–236 (1995).
Publisher: LAPACK project (Netlib hosting).
This source is credited to an organization.
Cited passages: DGTSV, LAPACK 3.12.1, Fortran lines 175–180: multiplier and two updates without row interchange; DGTSV, Purpose lines 34–39; DL argument lines 63–69; adjacent interchange lines 188–199; back solve lines 295–305.
Publisher: NPTEL.
Cited passages: Lecture 13, Thomas algorithm: opening historical attribution and Crank Nicolson motivation.
Publisher: Society for Industrial and Applied Mathematics.
Published in SIAM Journal on Numerical Analysis, volume 45, number 1, pp. 263–276.
Cited passages: §2.1, Corollary 2.1, printed pp. 264–265: Lipschitz continuously differentiable map, nonsingular state Jacobian, and a sufficiently small parameter increment; §2.2, Definition 2.2, printed p. 265: one-dimensional kernel of the state Jacobian and parameter derivative outside its range; §2.2, equations (2.2)–(2.5), printed pp. 265–266: unit tangent and hyperplane normalization; Corollary 2.3 gives local Newton convergence for sufficiently small steps.
Authored notes credited to André Massing, identified as André Jürgen Massing by the NTNU profile. Dated 3 October 2021, in the TMA4125/4130/4135 Mathematics 4N/D materials; the university is the host, rather than the author.
Cited passages: André Massing, Numerical solution of ordinary differential equations: One step methods, October 3, 2021, page 1, Example 1.1: Euler and Heun increment functions.
Collection of sources; individual chapter authors and dates are recorded below.
Lecture 7 course notes identify Gabriele Farina as instructor and record revisions through 15 March 2025. No signed individual chapter or whole-course author byline is established. The date is a revision date, distinct from the Spring 2025 offering.
Cited passages: Lecture 7, §L7.1.1, Definition L7.1, printed p. 3: the four KKT requirements; Lecture 7, §L7.1.3, Theorem L7.3, printed p. 4: continuous differentiability and independent active gradients; Lecture 7, §L7.1.3, Theorem L7.3, printed p. 4: independent active gradients.
University of California, Berkeley course, Fall 2009. Course instructor: James Demmel, verified by his faculty homepage. This association does not establish authorship of every course resource.
Instructor and course listing: people.eecs.berkeley.edu/~demmel/
Lecture notes in Math 221, Matrix Computations, Fall 2009, dated 10 November 2009 in the heading. The page has no explicit author byline. James Demmel is the verified course instructor; the University of California, Berkeley EECS faculty website hosts the notes. No separate publication date or institutional authorship is asserted.
Cited passages: Basic iterative methods, splitting and recurrence (*); spectral-radius lemmas and convergence-for-all-starts theorem; Jacobi and Gauss-Seidel component loops; strict row diagonal dominance, Theorem 1 and proof; 1D Dirichlet Poisson matrix and sine eigenvectors.
Additional cited passages: opening solver building blocks; Gauss-Seidel component loop, splitting, ordering remark and red-black scheduling; Theorem 1, strict row diagonal dominance; Theorem 3, SOR convergence for symmetric positive-definite matrices with the ω = 1 specialization. The lecture date and instructor association above remain distinct from author bylines and publication dates.
Official versioned routine documentation from the LAPACK project, hosted by Netlib. The Author section credits University of Tennessee, University of California Berkeley, University of Colorado Denver and NAG Ltd.; no individual author is inferred.
Version: LAPACK 3.12.1. The footer date 20 January 2025 is a Doxygen generation timestamp, not a verified code publication date.
Cited passages: Purpose: real symmetric positive-definite factorization; UPLO and INFO arguments; Author section: institutional credits.
Official versioned routine documentation from the LAPACK project, hosted by Netlib. The Author section credits University of Tennessee, University of California Berkeley, University of Colorado Denver and NAG Ltd.; no individual author is inferred.
Version: LAPACK 3.12.1. The footer date 20 January 2025 is a Doxygen generation timestamp, not a verified code publication date.
Cited passages: Purpose: complex Hermitian positive-definite factorization and conjugate transpose; Author section: institutional credits.
Historical research article by Claude Brezinski, published in Revue d’histoire des mathématiques 11 (2005), pp. 205–238. Numdam hosts the original journal article. The printed received date, 4 November 2004, and revised date, 11 May 2005, are distinct from publication.
Section 4 reproduces a primary manuscript authored by André-Louis Cholesky and dated Vincennes, 2 December 1910. Cholesky is the author of that manuscript; Brezinski is the author of the surrounding 2005 article. The manuscript date does not establish an exact invention date or a broad priority claim.
Cited passages: pp. 210–211: constrained geodetic corrections and the matrix ; p. 217: manuscript title, 2 December 1910 date and uncertainty about the exact invention date; §4, p. 229: the primary manuscript’s reported 56-equation altitude adjustment for Algerian triangulation and closing date. The primary manuscript transcription was inspected as text; no inspection of handwriting images is claimed.
University of California, Berkeley course, Fall 2023. The course homepage identifies James Demmel as instructor and labels the course Matrix Computations / Numerical Linear Algebra. The instructor role does not establish authorship of each resource.
Lecture notes in Math 221, Matrix Computations, Fall 2023, dated 1 December 2023 in the heading. No explicit author byline or institutional authorship is established. The University of California, Berkeley EECS faculty website hosts the notes; James Demmel is the course instructor. The lecture date is distinct from any publication or revision date.
Cited passages: PDF p. 1 heading and opening left/symmetric transformations; PDF p. 1, Preconditioned CG algorithm and equivalent symmetric system; PDF p. 1, goals (1) and (2), M = I and M = A comparison, example (1) Jacobi preconditioning; PDF p. 2, example (3) triangular factor solves; Course homepage, title and Instructor section, web lines 2–14.
Graduate course issued by the Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, and hosted by MIT OpenCourseWare. Course instructor: Pablo A. Parrilo; this teaching role does not establish authorship of every lecture note. Spring 2006 is the course term, not an online publication date.
Lecture note in Algebraic Techniques and Semidefinite Optimization, MIT 6.972, Spring 2006. The printed heading is Lecture 6; Resultants and Discriminants is a descriptive subject title. The heading credits Pablo A. Parrilo as lecturer and leaves the scribe unidentified. No individual authorship or editing credit is inferred. The Massachusetts Institute of Technology issues the course material; MIT OpenCourseWare hosts this copy.
Cited passages: printed pp. 6–1 to 6–2, §1 Resultants, Sylvester matrix and equation (1); printed p. 6–2, §2 Discriminants, Definition 2; printed p. 6–3, §3.1 Polynomial equations, elimination and backsubstitution. The printed date is the lecture date; no separate online publication or revision date is established.
University of California, Berkeley course. James Demmel is the instructor; this role does not establish authorship of each note. Spring 1996 is the course term.
Unsigned lecture notes dated 23 April 1996, hosted by the University of California, Berkeley. Neither personal nor institutional authorship is established.
Cited passages: Cholesky versus LU Decomposition, four phases; Left looking versus Right looking Cholesky; The Elimination Tree and Sources of Parallelism. Several later sections are marked under construction.
By Scott Kirkpatrick, Charles Daniel Gelatt Jr. and Mario P. Vecchi. Science 220(4598), 671–680 (13 May 1983).
Cited passages: pp. 672–673 and 675.
Cited passage: prime factor algorithm discussion, identifying the coprime-factor index map and absence of twiddle-factor multiplication. Search indexing exposed the relevant passage; direct fetching returned a gateway error during this pass. No revision date is asserted.
Published paper, BIT 3, 27–43; author byline Germund G. Dahlquist. Section 1 gives the constant-coefficient, first-derivative and coprimality assumptions; §2 defines A-stability and proves the order barrier. The university hosts the scan and is not its author.
Cited passages: Computational Routines, Linear Equations: symmetric indefinite factorization uses symmetric diagonal blocks of order one or two.
Consulted passage: Chapter3, Diffusion Equations, section3.1, explicit finite-difference discretization of one-dimensional diffusion and Forward Euler update. Publisher lists chapter pp207–322, first online22June2017, both authors. This is a whole-book source card; cite the chapter in its locator.
Consulted passages: section1.1, proper closed convex definition, printed p124; section1.2, projection onto a nonempty closed convex set, pp125–126; section3.2, resolvent interpretation, pp137–138; sections4.2–4.3, projected/proximal gradients and acceleration, pp148–152. The consulted PDF title page labels itself Foundations and Trends in Optimization1(3)(2013),123–231 and has a placeholder DOI; this draft label is not asserted as final journal-publication metadata.
Verified author list and archive history: arxiv.org/abs/1001.1549
Consulted passages: section1, equation(5), printed p2, symmetric second-order splitting; equation(11) and following negative-step discussion, printed pp3–4. Archive abstract records submission10January2010 and journal reference Bol.Soc.Esp.Mat.Apl.50(2010),47–61. The fetched PDF separately displays25April2022 on its title page; do not equate that displayed typesetting date with first publication.
Management Science13(7), pp492–498, published1March1967. Consulted publisher abstract, identifying the algorithm and its relationship between fractional and parametric programming; full paper not accessed. The wiki separately supplies its elementary compact-domain convergence proof.
Consulted Definition5.1 and equation(47), printed pp19–20; section5.1 and Theorem5.1, printed pp21–22, compactness/lower-semicontinuity hypotheses for existence. PDF title page displays18December2017, whereas archive version1 was posted30January2018; these are distinct dates.
Communications on Pure and Applied Mathematics 61, 1052–1117. DOI: doi.org/10.1002/cpa.20238 . Author-hosted PDF. Sections 1.1–1.3: action admissibility, noise convention, free-time quasipotential and geometric reformulation. Wiki uses drift a and covariance D to avoid the paper's a/b notation ambiguity; the time-reparameterization and gradient examples are explicitly derived.
Bulletin of the American Mathematical Society 49(1), 1–23. Primary PDF: www.ams.org/bull/1943-49-01/S0002-9904-1943-07818-4/S0002-9904-1943-07818-4.pdf . Cited for variational approximation by finite-parameter trial functions, including piecewise-linear constructions; no claim that Courant alone originated every finite-element method. Direct PDF access returned 403.
Authored technical account: www.scholarpedia.org/article/General_linear_methods . Scholarpedia2(4):2852; DOI:10.4249/scholarpedia.2852 . Cited definition section, equations(1)–(2), internal/external stages and inclusion of Runge-Kutta and linear multistep methods. Search-indexed primary text verified; one subsequent direct fetch timed out.
Official reference documentation: netlib.org/lapack/lug/node50.html and netlib.org/lapack/lug/node56.html . Cited sections: Eigenvalues, Eigenvectors and Schur Factorization; Eigenvalues, Eigenvectors and Generalized Schur Decomposition. These define real Schur blocks, homogeneous generalized eigenvalue pairs, infinite eigenvalues and the distinction between regular and singular pencils. Standalone qualified source card matches the existing LAPACK-reference-card convention; no personal authorship inferred from the generated-page footer.
SIAM, 2000. Author-hosted book description and sample chapters: people.maths.ox.ac.uk/trefethen/book.pdf . Fourier spectral differentiation and spectral collocation; independent aliasing example derived in article. Sample PDF has garbled text extraction; no unverified page quotation used.
Author-maintained institutional homepage: numerical-analysis and applied-mathematics appointments, links to books and software, portrait credited to Sarah Bird. Portrait people.maths.ox.ac.uk/trefethen/photo12small.jpg . Bibliographic use of full name is verified on the authors Spectral Methods in MATLAB page.
Official scipy.ndimage documentation: uniform filtering along one axis, window size, boundary extension modes and origin. The illustrative impulse response and continuous box self-convolution in the article are derived independently.
John Duchi, Elad Hazan and Yoram Singer; Journal of Machine Learning Research12(61),2121–2159(2011). Primary PDF: jmlr.org/papers/volume12/duchi11a/duchi11a.pdf
First-page full bylines verified. Section1.1, printed pp2122–2124, Eq1 and Eq5: cumulative gradient outer-product matrix, diagonal specialization and additive stabilization outside its square root. Used for mathematical mechanisms, not benchmark or convergence claims beyond their stated hypotheses.
Original ICLR2015 paper; inspected arXiv version9, dated30January2017. First-page bylines are Diederik P. Kingma and Jimmy Lei Ba; middle initial P. retained without expansion. Algorithm1 and section2, printed p2, define moment histories, corrections and epsilon placement; section3, printed p3, derives initialization correction under moment assumptions. Used for mathematical mechanisms rather than universal performance or convergence claims.
Author-maintained primary page. News identifies irace configuration software; General Info and Publications describe his computational-optimization research and books. The displayed last update is25May2018; it is not a birth date or a current-appointment assertion.
Primary institutional/author profile. Research interests identify combinatorial optimization, scheduling, routing and iterated local search. About my name explicitly gives Helena Ramalhinho Dias Lourenço and connects earlier H.R.Lourenço publications with the later H.Ramalhinho name. No initials are expanded by inference.
MathWorks Robust Control Toolbox documentation. Robust Stability, Robust Performance, and Mu Analysis: distinguishes stability over modeled uncertainty from meeting a specified performance level throughout that uncertainty range; examples use robuststab and robustperf.
MathWorks primary reference. Description, Range and Name properties: uncertain real parameters have nominal values and specified ranges; named repeated blocks preserve the identity of an uncertain element when models are combined.
MathWorks primary reference. Description: robust stability margin is relative to the uncertainty specified in the model; returned bounds concern the actual margin, and a margin exceeding1 certifies stability throughout the modeled uncertainty.
Description and Uncertain Dynamics examples: linear time-invariant dynamic uncertainty with frequency-response gain bounds; shaping filters can encode stronger uncertainty at high frequencies.
Description: distinguishes impulse-response H2 norm from peak frequency-response gain; for stable systems the latter equals the H-infinity norm. The input/output signal norms must be distinguished from the software name used for a transfer-function norm.
Input argument utype: InputMult gives Pnom*(I+W1DeltaW2), OutputMult gives (I+W1DeltaW2)Pnom, and Additive gives Pnom+W1Delta*W2. The shaping filters fit uncertainty across frequency.

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