{ "cells": [ { "cell_type": "markdown", "id": "81b1d2f0", "metadata": {}, "source": [ "---\n", "title: \"Zero Stability\"\n", "subtitle: \"Lecture 7: Zero-stability of Runge-Kutta and multistep methods\"\n", "date: 2026-02-16\n", "abstract-title: Overview\n", "abstract: | \n", " (1) Recap, A2, \n", " (2) Zero stability of multistep methods, \n", " (3) Discussion of A3. \n", "format:\n", " html:\n", " other-links:\n", " - text: This notebook\n", " href: L7.ipynb\n", "---" ] }, { "cell_type": "markdown", "id": "63cf0867", "metadata": {}, "source": [ "::: {.callout-note}\n", "\n", "I encourage you to play around with the juptyer notebook for this lecture - you can copy the code with the ```this notebook``` button on the side of this page.\n", "\n", ":::\n", "\n", "::: {.callout-warning}\n", "\n", "These notes are mainly a record of what we discussed and are not a substitute for attending the lectures and reading books! If anything is unclear/wrong, let me know and I will update the notes.\n", "\n", ":::\n", "\n", "::: {.callout-tip}\n", "\n", "This lecture is mostly based on @Burden section 5.6 and @FNC section on zero stability,\n", "\n", ":::" ] }, { "cell_type": "code", "execution_count": 2, "id": "db6fe346", "metadata": {}, "outputs": [], "source": [ "#| echo: false\n", "\n", "# IF YOU ARE READING THIS, THANK YOU\n", "# FOR DOWNLOADING THE LECTURE NOTES.\n", "# THE FIRST PERSON TO LET ME KNOW,\n", "# WINS SOME CHOCOLATES OF YOUR CHOICE\n", "\n", "using Plots, LaTeXStrings, OrdinaryDiffEq" ] }, { "cell_type": "markdown", "id": "5ea01014", "metadata": {}, "source": [ "## Recap\n", "\n", "Recall that we are considering IVPs: seek $u :[0,T] \\to \\mathbb R$ such that\n", "\n", "\\begin{align}\n", " &u(0) = u_0 \\nonumber\\\\\n", " &u'(t) = f\\big( t, u(t) \\big). \\tag{IVP}\n", "\\end{align}\n", "\n", "We will suppose that $f$ is continuous on $[0,T] \\times \\mathbb R$ and Lipschitz in the second argument and so the problem is well-posed and there exists a unique solution to $(\\text{IVP})$. Recall *one-step methods*: \n", "\n", "\\begin{align}\n", " u_{j+1} = u_j + h \\phi(t_j, u_j; h)\n", " \\tag{1-step}\n", "\\end{align}\n", "\n", "where $t_j = j \\frac{T}{n} = j h$ defines the *mesh*. We saw last week that, if the local truncation error is $\\tau_{j+1} = O(h^p)$ as $h\\to 0$ (i.e. if the method is *consistent* with *order of accuracy $p$*) and $|\\frac{\\partial \\phi}{\\partial u}| \\leq L$ on $[0,T] \\times \\mathbb R$ (i.e. the method is *zero-stable*), then we have the error bound \n", "\n", "\\begin{align}\n", " |u(t_j) - u_j| \\leq \\frac{Ch^p}{L} ( e^{Lt_j} - 1)\n", "\\end{align}\n", "\n", "(i.e. the method is *convergent*). This result applies to Runge-Kutta methods:" ] }, { "cell_type": "code", "execution_count": 3, "id": "a97dee77", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "RK (generic function with 1 method)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function RK( u0, f, T, n, A, b, c )\n", " h, t = T/n, 0:T/n:T \n", " u = fill(float(u0), n+1)\n", " s, = size(A)\n", " s = s+1 \n", " k = fill(float(u0), s)\n", " for j = 1:n\n", " k[1] = h * f( t[j], u[j] )\n", " for i = 1:s-1 \n", " k[i+1] = h * f( t[j] + h * c[i], u[j] + sum( A[i,ℓ] * k[ℓ] for ℓ ∈ 1:i ) )\n", " end\n", " u[j+1] = u[j] + sum( b[ℓ] * k[ℓ] for ℓ ∈ 1:s )\n", " end\n", " return u\n", "end " ] }, { "cell_type": "markdown", "id": "b8ee6891", "metadata": {}, "source": [ "## Multistep methods\n", "\n", "@Burden section 5.6\n", "\n", "All the methods we have seen so take the form $u_{j+1} = u_j + h \\phi( t_j, u_j; h)$. These are known as $1$-step methods because $u_{j+1}$ is only given as a function of $1$ previously computed value $u_j$. Multistep methods hope to improve efficiency by using the history of the solution $\\{u_j, u_{j-1}, \\dots, u_{j-m+1}\\}$ for some $m \\in \\mathbb N$ to compute the next term $u_{j+1}$. Linear multistep methods produce $u_{j+1}$ as a linear combination of $\\{ u_{i} \\}$ and $\\{ f(t_{i}, u_{i}) \\}$:\n", "\n", "::: {#def-mstep}\n", "# Linear multistep method\n", "\n", "A linear $m$-step method is of the form:\n", "\n", "\\begin{align}\n", " u_{j+1} &= \\alpha_{m-1} u_{j} + \\alpha_{m-2} u_{j-1} + \\cdots + \\alpha_{0} u_{j-m+1} \\nonumber\\\\\n", " %\n", " &+ h \\big[ \\beta_m f(t_{j+1}, u_{j+1}) + \\beta_{m-1} f(t_{j}, u_{j}) + \\cdots + \\beta_0 f(t_{j-m+1}, u_{j-m+1})\\big]\n", "\\end{align}\n", "\n", "for some coefficients $\\alpha_0,\\dots,\\alpha_{m-1}$ and $\\beta_0, \\dots, \\beta_{m}$. \n", "\n", "If $\\beta_m = 0$, the method is *explicit* ($u_{j+1}$ is given explicitly),\n", "\n", "If $\\beta_m \\not= 0$, the method is *implicit* ($u_{j+1}$ solves a non-linear equation that must be solved).\n", "\n", ":::\n", "\n", "::: {.callout-note}\n", "\n", "For $1$-step methods, we started from $u_0$ given by the equation. \n", "\n", "Now, we need to initiate $u_0,\\dots,u_{m-1}$ in order to define $u_{m}$. This can be done by e.g. using a RK method.\n", "\n", ":::\n", "\n", "::: {.callout-note}\n", "\n", "We can store the history $f(t_{j-1}, u_{j-1}), \\dots, f(t_{j-m+1}, u_{j-m+1})$ so that (in the explicit case) to evaluate $u_{j+1}$ we only need to compute one function evaluation $f(t_{j}, u_{j})$.\n", "\n", ":::\n", "\n", "Here is a basic implementation which uses ```RK4``` to compute $u_1,\\dots,u_{m-1}$. In the implicit case, we need to solve a nonlinear problem in 1d (See [Chapter 2](https://math5485.thomaslabs.co.uk/L4%20Solving%20nonlinear%20equations%20in%201d.html) of Math 5485 for the details). To do this, we use ```Roots``` (Exercise: what method does this package use?)," ] }, { "cell_type": "code", "execution_count": 4, "id": "968d7f1d", "metadata": {}, "outputs": [], "source": [ "using Roots" ] }, { "cell_type": "code", "execution_count": 5, "id": "f1f527a8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "linearMultistep (generic function with 1 method)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function linearMultistep( u0, f, T, n, α, β)\n", " m, h, t = length(α), T/n, 0:T/n:T \n", " u = fill(float(u0), n+1)\n", "\n", " # initiate u_1,...,u_m-1 using RK4\n", " if (m > 1)\n", " u[1:m] = RK( u0, f, (m-1)*h, m-1, \n", " [1/2 0 0 ; 0 1/2 0 ; 0 0 1],\n", " [1/6 1/3 1/3 1/6], [1/2 1/2 1] ) \n", " end\n", "\n", " f_hist = [ f(t[m-ℓ],u[m-ℓ]) for ℓ ∈ 1:m-1 ]\n", " for j = m:n\n", " f_hist = [ f(t[j],u[j]), f_hist[1:m-1]... ]\n", " if (length(β) == m)\n", " u[j+1] = sum( α[m-ℓ] * u[j-ℓ] + h * β[m-ℓ] * f_hist[ℓ+1] for ℓ ∈ 0:(m-1) )\n", " else\n", " r = x -> x - h * β[m+1] * f(t[j+1], x) - sum( α[m-ℓ] * u[j-ℓ] + h * β[m-ℓ] * f_hist[ℓ+1] for ℓ ∈ 0:(m-1) )\n", " u[j+1] = find_zero( r, u[j] )\n", " end\n", " end \n", " \n", " return u\n", "end " ] }, { "cell_type": "markdown", "id": "24e882d8", "metadata": {}, "source": [ "::: {#exm-AB}\n", "# Adams-Bashforth (AB)\n", "\n", "AB methods are explicit ($\\beta_{m} = 0$) with $\\alpha_{m-1} = 1$ and $\\alpha_{m-2} = \\cdots = 0$. They are chosen to have order $p=m$ and denoted $\\text{(AB}p\\text{)}$:\n", "\n", "\\begin{align}\n", " \\tag{AB1}\n", " &m=1, \\quad \\beta_0 = 1 \n", "\\\\\n", " \\tag{AB2}\n", " &m=2, \\quad \\beta_1 = \\frac32, \\quad \\beta_0 = -\\frac12 \n", "\\\\\n", " \\tag{AB3}\n", " &m=3, \\quad \\beta_2 = \\frac{23}{12}, \\quad \\beta_1 = -\\frac{16}{12}, \\quad \\beta_0 = \\frac5{12} \n", "\\end{align}\n", "\n", ":::\n", "\n", "::: {#exr-AB1}\n", "\n", "Notice that $\\text{(AB1)}$ is Euler's method.\n", "\n", ":::\n", "\n", "We define the local truncation error in an analogous way to $1$-step methods:\n", "\n", "::: {#def-LTE}\n", "\n", "The local truncation error of a linear multistep method with coefficients $\\alpha_{m-1}, \\dots, \\alpha_0$ and $\\beta_{m},\\dots,\\beta_0$ is given by \n", "\n", "\\begin{align}\n", " \\tau_{j+1}(h) \n", " &= \n", " \\frac1h \\Big[\n", " u(t_{j+1}) - \\sum_{i=0}^{m-1} \\alpha_{m-1-i} u(t_{j-i}) \n", " \\Big] \\nonumber\\\\\n", " %\n", " &\\quad - \\sum_{i=0}^m \\beta_{m-i} f\\big( t_{j+1-i}, u(t_{j+1-i}) \\big)\n", "\\end{align}\n", "\n", "We say the multistep method is *consistent* if $\\max_j \\tau_{j+1}(h) \\to 0$ as $h\\to 0$. \n", "\n", "We say the multistep method has *order of accuracy $p$* if $\\tau_{j+1}(h) = O(h^p)$ as $h\\to 0$.\n", "\n", ":::\n", "\n", "::: {#exr-AB1}\n", "\n", "Show that $\\text{(AB2)}$ has order of accuracy $2$.\n", "\n", ":::\n", "\n", "::: {#exm-AM}\n", "# Adams-Moulton (AM)\n", "\n", "AM methods are implicit ($\\beta_{m} \\not= 0$) with $\\alpha_{m-1} = 1$ and $\\alpha_{m-2} = \\cdots = 0$. Since there is another degree of freedom ($\\beta_m\\not=0$), $m$-step implicit methods can have order of accuracy $p = m+1$:\n", "\n", "\\begin{align}\n", " \\tag{AM1}\n", " &m=1, \\quad \\beta_1 = 1, \\quad \\beta_0 = 0 \n", "\\\\\n", " \\tag{AM2}\n", " &m=1, \\quad \\beta_1 = \\frac12, \\quad \\beta_0 = \\frac12 \n", "\\\\\n", " \\tag{AM3}\n", " &m=2, \\quad \\beta_2 = \\frac{5}{12}, \\quad \\beta_1 = \\frac{8}{12}, \\quad \\beta_0 =- \\frac1{12} \n", "\\end{align}\n", "\n", "Here, we use the naming convention $(\\text{AM}p)$ where $p$ is the order of accuracy.\n", "\n", ":::\n", "\n", "::: {#exr-AM}\n", "\n", "Write down the formulas for $(\\text{AM}1)$, $(\\text{AM}2)$, $(\\text{AM}3)$.\n", "\n", ":::\n", "\n", "::: {.callout-note}\n", "\n", "$(\\text{AM}1)$ is also called *backward's Euler* because you can derive it from $u'(t_{j+1}) = f(t_{j+1}, u_{j+1})$ and replace the derivative with the *backwards difference* $\\frac{u_{j+1} - u_j}{h}$.\n", "\n", "$(\\text{AM}2)$ is also called the *trapezoid rule* or *Crank-Nicolson*\n", "\n", ":::" ] }, { "cell_type": "markdown", "id": "403e3bbd", "metadata": {}, "source": [ "::: {#exm-1}\n", "\n", "Using our function ```linearMultistep()```, we can try and numerically solve \n", "\n", "\\begin{align}\n", " u(0) &= 0 \\nonumber\\\\\n", " u'(t) &= \\cos u(t) + \\sin t\n", "\\end{align}\n", "\n", "on $[0, 5]$. Again, we plot the solution using a built-in function with a small tolerance so we have something to compare with." ] }, { "cell_type": "code", "execution_count": 6, "id": "4db95d71", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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Inf : cos(u) + sin(t) \n", "\n", "ivp = ODEProblem((u,p,t)->f(t,u), u0, (0., T))\n", "sol = solve(ivp, Tsit5(), reltol=1e-15, abstol=1e-15)\n", "\n", "u1 = linearMultistep(u0, f, T, n, [0 1], [-1/2 3/2]) # AB2\n", "u2 = linearMultistep(u0, f, T, n, [1], [1/2 1/2]) # AM2\n", "\n", "plot(sol, \n", " label=\"Tsit5()\", \n", " xlabel=L\"t\", ylabel=L\"u(t)\")\n", "\n", "plot!(0:T/n:T, u1, m=3, label=\"AB2\")\n", "plot!(0:T/n:T, u2, m=3, label=\"AM2\")" ] }, { "cell_type": "markdown", "id": "cee513b0", "metadata": {}, "source": [ "
\n", "\n", "We plot the errors of various methods that we have seen:" ] }, { "cell_type": "code", "execution_count": 7, "id": "79eb5db1", "metadata": {}, "outputs": [ { "data": { "image/png": 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= linearMultistep(u0, f, T, n, [1], [0 1]) # Backwards Euler\n", "\n", " # order 2\n", " u[:,3] = linearMultistep(u0, f, T, n, [0 1], [-1/2 3/2]) # AB2\n", " u[:,4] = linearMultistep(u0, f, T, n, [1], [1/2 1/2]) # AM2 = trapezoid\n", " \n", " # order 4\n", " u[:,5] = linearMultistep(u0, f, T, n, [0 0 0 1], [-9/24 37/24 -59/24 55/24]) # AB4\n", " u[:,6] = linearMultistep(u0, f, T, n, [0 0 1], [1/24 -5/24 19/24 9/24]) # AM4 \n", " u[:,7] = RK( u0, f, T, n, \n", " [1/2 0 0 ; 0 1/2 0 ; 0 0 1],\n", " [1/6 1/3 1/3 1/6], [1/2 1/2 1] ) # RK4\n", "\n", " mesh = 0:T/n:T\n", " for i ∈ 1:7\n", " errs[ℓ,i] = maximum( @. abs( u[:,i] - sol(mesh) ) )\n", " end\n", "end\n", "\n", "plot(nn, errs[:,1:7];\n", " m=3, label=[\"AB1 = Euler\" \"AM1 = Backwards Euler\" \"AB2\" \"AM2 = Trapezoid\" \"AB4\" \"AM4\" \"RK4\"], \n", " xaxis=(:log10, L\"n\"), yaxis=:log10,\n", " title=\"Error\", legend=:bottomleft)\n", "plot!( nn, (1/2)*errs[end,1]*(nn/nn[end]).^(-1), \n", " label=L\"O(n^{-1})\", linestyle=:dash, primary=false )\n", "plot!( nn, (1/2)*errs[end,4]*(nn/nn[end]).^(-2), \n", " label=L\"O(n^{-2})\", linestyle=:dash, primary=false )\n", "plot!( nn, (1/2)*errs[end,7]*(nn/nn[end]).^(-4), \n", " label=L\"O(n^{-4})\", linestyle=:dash, primary=false)" ] }, { "cell_type": "markdown", "id": "93d1e5e7", "metadata": {}, "source": [ "Here, we can see that all the methods introduced above are convergent (in this particular case). But why?\n", "\n", ":::\n", "\n", "## Zero-stability of Linear Multistep Methods\n", "\n", "We saw that, if $|\\frac{\\partial \\phi}{\\partial u}\\big| \\leq L$, then the 1-step methods (in particular Runge-Kutta methods) are convergent and their rate of convergence is given by the order of accuracy (i.e. the rate of convergence is given by the local truncation error). This is not necessarily true for general linear multistep methods:\n", "\n", "::: {#exm-2}\n", "\n", "Here, we return to the equation from @exm-1 but now use the method\n", "\n", "\\begin{align}\n", " u_{j+1} &= (1-\\alpha) u_j + \\alpha u_{j-1} \n", " \\nonumber\\\\\n", " &\\,\\, + \\frac{h}{2} \\big( (\\alpha + 3) f_j + (\\alpha-1) f_{j-1} )\n", " %\n", " \\tag{$\\alpha2$}\n", "\\end{align}\n", "\n", "where $f_i := f( t_i, u_i )$.\n", "\n", "Note: calling this method $(\\alpha2)$ is non-standard notation!\n", "\n", "::: {#exr-2}\n", "\n", "Show that this method has order of accuracy $p=2$. Extra: for what $\\alpha$ is this method 3rd order accurate? \n", "\n", ":::\n", "\n", "What do you expect to happen if we apply this method with different choices of $\\alpha$?" ] }, { "cell_type": "code", "execution_count": 11, "id": "5eb4916b", "metadata": {}, "outputs": [ { "data": { "image/png": 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"\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n1, n2 = 20, 100\n", "\n", "α = -1.001\n", "\n", "u1 = linearMultistep(u0, f, T, n1, [α, 1-α], [(α-1)/2, (α+3)/2]) \n", "u2 = linearMultistep(u0, f, T, n2, [α, 1-α], [(α-1)/2, (α+3)/2]) \n", "\n", "P = plot(sol, \n", " label=\"Tsit5()\", \n", " xlabel=L\"t\", ylabel=L\"u(t)\")\n", "\n", "plot!(0:T/n1:T, u1, m=3, label=\"α = $α, n = $n1\")\n", "plot!(0:T/n2:T, u2, m=3, label=\"α = $α, n = $n2\", ylims=(0,3))\n", "\n", "nn = [round(Int, 10^ℓ) for ℓ ∈ 1:0.5:5]\n", "errs = zeros(length(nn))\n", "for (ℓ,n) ∈ enumerate(nn)\n", " u = linearMultistep(u0, f, T, n, [α, 1-α], [(α-1)/2, (α+3)/2]) \n", " mesh = 0:T/n:T\n", " errs[ℓ] = maximum( @. abs( u - sol(mesh) ) )\n", "end\n", "\n", "P′ = plot(nn, errs;\n", " m=3, xaxis=(:log10, L\"n\"), yaxis=(:log10, \"Error\"),\n", " legend=false)\n", "\n", "plot( P, P′, layout=(1,2), size=(1000,500))" ] }, { "cell_type": "markdown", "id": "fa6880e2", "metadata": {}, "source": [ "
\n", "\n", "Aim of today: understand what is happening here!\n", "\n", ":::\n", "\n", "In order to understand what is happening here, we need to define the following *characteristic polynomials*:\n", "\n", "::: {#def-characteristic}\n", "\n", "We define the *characteristic polynomials*\n", "\n", "\\begin{align}\n", " \\rho(z) &= z^m - \\alpha_{m-1} z^{m-1} - \\alpha_{m-2} z^{m-2} - \\cdots - \\alpha_0 \\nonumber\\\\\n", " \\sigma(z) &= \\beta_m z^m + \\beta_{m-1} z^{m-1} + \\cdots + \\beta_0. \n", "\\end{align}\n", "\n", "These are also called *generating polynomials*.\n", "\n", "::: \n", "\n", "::: {#exr-}\n", "\n", "Write down the characteristic polynomials associated to the method $(\\alpha2)$. What are the roots of $\\rho$ in this case.\n", "\n", ":::\n", "\n", "We now introduce the following (very simple) IVP:\n", "\n", "\\begin{align}\n", " u(0) &= u_0 \\not= 0 \\nonumber\\\\\n", " u'(t) &= 0 \\tag{test}.\n", "\\end{align}\n", "\n", "Notice that $u(t) = u_0$ is the exact solution to this equation. When approximating $(\\text{test})$ with our linear multistep method, we obtain the difference equation \n", "\n", "\\begin{align}\n", " u_{j+1} = \\alpha_{m-1} u_j + \\alpha_{m-2} u_{j-1} + \\dots + \\alpha_0 u_{j+m-1}.\n", "\\end{align}\n", "\n", "Suppose that $\\zeta_0$ is a root of $\\rho$. Then, $u_{j} := (\\zeta_0)^j$ solves $(6)$. In fact, if all roots, $\\zeta_0,\\dots,\\zeta_{m-1}$, of $\\rho$ are simple, then the general solution to $(6)$ is given by \n", "\n", "\\begin{align}\n", " u_j := c_0 (\\zeta_0)^j + \\cdots + c_{m-1} (\\zeta_{m-1})^j\n", "\\end{align}\n", "\n", "for some constants $c_0, \\cdots, c_{m-1}$. By consistency of the multistep method, we must have $\\alpha_0 + \\dots + \\alpha_m = 1$ and so $u_j := u_0$ must be a solution of $(6)$. As a result, the general solution to $(6)$ is of the form \n", "\n", "\\begin{align}\n", " u_j := u_0 + c_1 (\\zeta_1)^j + \\cdots + c_{m-1} (\\zeta_{m-1})^j\n", "\\end{align}\n", "\n", "where $1,\\zeta_1,\\dots,\\zeta_{m-1}$ are the roots of $\\rho$ and $c_1,\\dots,c_{m-1}$ are some constants. The constants $c_1,\\dots,c_{m-1}$ are in general non-zero due to round-off errors. This error grows exponentially unless $|\\zeta_j| \\leq 1$ for each of the roots $\\zeta_j$ of $\\rho$.\n", "\n", "::: {#def-rootcondition}\n", "\n", "We say a linear multistep method satisfies the *root condition* if all roots $\\zeta$ of the characteristic polynomial $\\rho$ satisfy $|\\zeta|\\leq 1$ and, if $|\\zeta| = 1$, then $\\zeta$ is a simple root.\n", "\n", ":::\n", "\n", "::: {#exr-alpha}\n", "\n", "For what $\\alpha$ does $(\\alpha2)$ satisfy the root condition?\n", "\n", ":::\n", "\n", "\n", "::: {#thm-convergence}\n", "\n", "A linear multistep method is zero-stable if and only if it satisfies the root condition. \n", "\n", "A consistent linear multistep method is convergent if and only if it is zero-stable.\n", "\n", ":::\n", "\n" ] }, { "cell_type": "markdown", "id": "b94ee96d", "metadata": {}, "source": [ ":::{.callout-tip}\n", "# TO-DO\n", "\n", "* Assignment 3: Due next Wednesday 11:59 PM,\n", "* Make sure you are up to date with @Burden sections 5.1 - 5.6, @FNC [zero stability](https://fncbook.com/zerostability/) \n", "* (Sign-up to office hours if you would like)\n", " \n", "Next: Chapter 2: Iterative Methods in Matrix Algebra\n", "\n", "* Read: sections 7.1 - 7.3 of @Burden\n", "\n", ":::" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.11", "language": "julia", "name": "julia-1.11" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }